I wanna see if I can clear some confusion. Some people are confused that this statement is not reversible. The statement can be edited to be reversible if you change "only if" to "if AND only if". For example: "(You can play video games) IF AND ONLY IF (you've finished your homework)" is a reversible statement. This is because it secretly holds several statements in one. "if AND only if" combines the forward version of a statement with it's backward version. SO! If you have "(You can play video games) IF (you've finished your homework)", you have V->H. If you have "(You can play video games) ONLY IF (you've finished your homework)", you have H->V. BUT! if you have "(You can play video games) IF AND ONLY IF (you've finished your homework)", you have the conjunction of both; (V->H)^(H->V) which is the same as saying VH. Hope I could help someone. It definitely helped me typing it down.
+William Spaniel But Sir, In Example 2, both the statement and the converse are true If you can play video games, than you must've done your HW so V=>H and if you did your HW, then you can play video games V holds and H holds too, we express it with the notation VH In the statement V, we're talking about the possibility of playing video games, it'll only be possible if you did your HW, but you don't actually have to play video games, but it's still true that it's possible if you'd done your HW Please correct me if I'm wrong
The only one that got me confused was #2. Are they not reversible? 1. If you have finished your homework, you can play video games. (Because wouldn't finishing your homework automatically allow you to play video games, even if you don't?) 2. You can only play video games if your homework is finished. So to me it seems like V H Although I don't think it would work if you take out the "Can".
"wouldn't finishing your homework automatically won't allowed you to play games" Cause there's a IF only if homework is finished then game. If you convert that sentence into IF-THEN, then you'll come up with V=>H
Just because you've finished your homework doesn't mean the electricity is running and the internet works. But if nothing's stopping you then that includes the homework, which must therefore be 'done'
Great video, but could explain why it doesn't go the other way, like how License -> Driver test, but not Driver Test -> license, because you can pass the driving test and still not get it for failing vision test or have it rewoked.
For the example 2, I wrote ~H => ~V. Correct me if I'm wrong, but doesn't the sentence mean to say that if you don't finish your homework, you cannot play Video Games (as an order, which I have heard so many times btw).
1) P=>(O^C) 2) V=>H //I am learning programming and it's weird to me that logic should be express this way since it would need to be H=>V in a program. 3) L=>T //Ok this frustrates me since the sentences get flipped in this case. It seems to me it should be T=>L - If the driver's test is passed, then a driver's license can be had. 4) ~F=>M 5) U=>F
I agree with your second answer! logically it should be H => V / because you need to finish your HW first THEN you can play the game or whatever you want
"Passing a driver's test is required to have a driver's license." This states that passing a driver's test is a necessary precondition for having a driver's license, but that doesn't mean that there aren't other unknown preconditions for having a driver's license. If I say, "Getting a driver's license requires you to *pass a driver's test* and you must pass a substance abuse and traffic laws course" then the statement, "If you have a driver's license, you have passed a driver's test" because it is a necessary precondition for having a driver's license. However, the reciprocal, "If you have passed a driver's test, you have a driver's license" is not true because it has not shown that you have completed the second necessary precondition, which is passing a substance abuse and traffic laws course. "Well, the statement, 'If you have a driver's license, you have passed a driver's test' is not true because it also doesn't show that you have completed the second requirement." This is false because it starts at the assumption that you have a driver's license. If you have a driver's license then you have obviously completed both of the necessary preconditions, a driver's test being one of them. The statement is true because, even though it doesn't state the second requirement of getting a driver's license, it is still obviously true that you have fulfilled the first precondition for the driver's license.
Example #1: P=>(O^C) // got it right! Example #2: I think both "If you've finished your homework, then you can play video games." and "If you can play video games, then you've finished your homework." could work. Maybe both H=>V and V=>H are valid so it's some kind of reciprocal condition? Such as (H=>V)^(V=>H). // aaand I was wrong. Example #3: "If one has a driver's license, the one passed the test" maybe? So L=>T // correct! Example #4: "If one doesn't want to pay absurd bank fees, then it is necessary for one to mantain a $1,000 balance". I'm guessing the first statement has to be considered as a negative version of "one wants to pay absurd bank fees"; my answer is ~F=>M // correct =D. Example #5: "If one has finished Game Theory 101, then one has a basic understanding of game theory". I'll go ahead and answer F=>U // I was right!
I also thought the 2nd example was a biconditional until i came across a comment that basically says: -'Can' means that you have the OPTION to play video games - But 'Can' only applies if you assume that the video game is working. The video game has to work in order for you to 'Can' play it - So (H=>V)^(V=>H) is only true if you assume that the video game is working. - Since it is not stated that the video game is working H=>V is false - If you CAN play the video game, it necessarily means that it is working AND that you have finished your homework. therefore only V=>H is true
This is my attempt at answering each examples: Example 1: P ^ O v C Example 2: H = V Example 3: T = L Example 4: M = F Example 5: F = U I guess I got most of them wrong except for the last one. I still keep on switching each of them up.
The operations team were fully staffed. All the staff were Vulcans. All Vulcans are logical. Therefore all the operations team were Logical Operators. If V & O than L
i have a question could i write these sentences (you can play video only if you have finished the home work ) with an exclusive or (A or ~B)or (~A or B) ?
The first example cannot be biconditional because obviously there are many adults that fit this description that are not the president of the United States. So it can only be written as P -> (O ^ C)
GOT IT. Just because you've finished your homework doesn't mean the electricity is running and the internet works. But if nothing's stopping you then that includes the homework, which must therefore be 'done' or rendered moot by the dog, which could be considered 'done' in a manner of speaking but i digress.
It's understood when V refers to the playing itself, but what if V refers to the possibility/ability of playing the videogames, i.e. "you CAN play videogames"? Couldn't it ne written as "H=>V"?!
I really dont get the statement at the end that P -> Q = -P v Q Looking at example 5 for instance, if finishing game theory 101-> understand game theory This implies that one does not finish game theory OR they understand game theory?? What if they underatand game theory from an alternative means? Or what about if someone did finish game theory 101 but didnt underatand it. Does all of my confusion have to do witb the first proposition not being true itself?
For example #4, I think it would be F -> M. Here are my reasoning: F: Not paying absurd bank fees M: Maintaining a $1,000 balance Therefore: F -> M (If you are not paying absurd bank fees, then you are maintaining a $1,000 balance) We cannot say ~F -> M because it means (If you ARE [negating the negative] paying absurd bank fees, then you ARE maintaining a $1,000 balance) We can say ~F -> ~M because it means (If you ARE paying absurd bank fees, then you ARE NOT maintaining a $1,000 balance) Please reply with regards to my correctness. Thanks :)
+Syed Ameed It looks like your mistake is identifying simple sentences. We can't use F to represent "you are not paying absurd bank fees" because "you are not paying absurd bank fees" is not a simple sentence. "You are paying absurd bank fees" is a simple sentence, though, and we can turn it into the antecedent of the conditional by adding a negation. Thus, ~F at the start.
William Spaniel Does the antecedent needs to be a simple sentence? I thought that we can use any statements, once it's closed and can be expressed as true or false.
+Syed Ameed The antecedent does not need to be a simple sentence. But single letters (like F) must be simple sentences. "I do not pay fees" = F isn't good because "I do not pay fees" is not a simple sentence. "I pay fees" is, however. So that's why we have ~F in the example.
You probably dont give a shit but does anyone know of a tool to get back into an instagram account?? I somehow lost the login password. I would love any tricks you can offer me
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1) P => O ^ C 2) V => H ..(my logic behind this is that if your are playing video game then you have already finished your homework so upon translating it I get if V is true then H is true... hope fully I am right)...YES 3) L =>T (If you have a driver's license then you passed a driver's test) 4) ~F => M ( if you are not paying absurd bank fees then you are maintaining a $1000 balance) 5) F => U ( If you finished GT 101 then you have a basic understanding of GT)
if the statement is p-"I go to the beach whenever it is a sunny summer day" then it's converse is "if i go to the beach then it is a sunny summer day" but i wanna know that if i write the converse of the statement p is- "its a sunny summer day whenever i go to beach" and the contrapositive is- "its not a sunny summer day whenever i dont go to the beach" will it be wrong? if yes then i wanna know why?
The unfair answer is "because that's not what the statement said." A more helpful answer is passing a driver's test does not guarantee having a license---they might have failed the vision test or been ticketed for a DUI and had their license revoked.
Plz help me out! passing a driver’s Test is required to have a driver’s License. L=>T Finishing game theory 101 is sufficient to have a basic Understanding of game theory. F=>U Grammatically both sentences are the same, but we convert them differently. So how do we distinguish? What seems to work is applying the following structure: Left part is true => Right part is ALWAYS true Then: Conversion A: Left part (understanding game theory) => Right part (finishing game theory 101) is NOT always true, one might learn elsewhere Conversion B: Left part (finishing game theory 101) => Right part (understanding game theory) is ALWAYS True, no contraction here Thus: Conversion B is correct
So basically the first part is always the "if" part and the second part of the sentence is always the "then" part? (Except when you use 'required for'?)
+Maderra -4 No, that would mean that maintaining a $1,000 balance ensures that you won't pay absurd bank fees. The English sentences leave open the possibility that one could have that much in the account but still pay absurd fees for some other reason.
@@Gametheory101 no it doesn't, the English statement says to avoid absurd BANK FEE'S (all encompassing term), it is necessary to maintain a $1,000 dollar balance. To void M=>~f, you should specify what fee you're avoiding, otherwise the statement covers all possible fee's. the absurd complicates things, you could read it as expensive or unwarranted, but it is not a condition, it is a description of the bank fee's It should also say a minimum of $1,000 balance; otherwise you could say that you get bank fee's for having over $1,000 in the account and who would bank at a place like that? :P
@@shitMountain "To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary *maintain a 1000 balance,* Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being *maintaining a 1000 balance.* Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of *maintaining a 1000 balance,* just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have *maintained a 1000 balance* still remains true."
can you please explain to me how "if p, then q" has the same logical meaning as "q unless ~p" ??? It's been driving me crazy. I can't understand it in terms of sentences and in terms of truth tables too
I think example #3 is incorrect. in writing if - then statement from a sentence, the subject remains the subject and the predicate also remains as the predicate.
"Passing a driver's test is required to have a driver's license." This states that passing a driver's test is a necessary precondition for having a driver's license, but that doesn't mean that there aren't other unknown preconditions for having a driver's license. If I say, "Getting a driver's license requires you to pass a driver's test and you must pass a substance abuse and traffic laws course" then the statement, "If you have a driver's license, you have passed a driver's test" because it is a necessary precondition for having a driver's license. However, the reciprocal, "If you have passed a driver's test, you have a driver's license" is not true because it has not shown that you have completed the second necessary precondition, which is passing a substance abuse and traffic laws course. "Well, the statement, 'If you have a driver's license, you have passed a driver's test' is not true because it also doesn't show that you have completed the second requirement." This is false because it starts at the assumption that you have a driver's license. If you have a driver's license then you have obviously completed both of the necessary preconditions, a driver's test being one of them. The statement is true because, even though it doesn't state the second requirement of getting a driver's license, it is still obviously true that you have fulfilled the first precondition for the driver's license.
P => O ^ C H => V [Correction: Reversed] L => T M => ~F [Correction: Got it backwards again] U => F [Correction: Again Again backwards] I guess I'll have to work on these things
(P -> (O^C H -> V (Guess I got that wrong, but I used the same way: If you finished your homework, you can play videogames). L -> T (reasoning being that if you have a license, you must have passed a driver's test, it must be true.) M -> ~F (if you have maintained 1k bal, you will not pay absurd fees.) Guess I got that wrong too lol, probably because it's not always the case that when you maintain a 1k bal it must mean you didn't pay absurd fees. Maybe it's just your salary etc. Should work on it. F -> U (wasn't too sure about this one, cause it isn't a sure outcome.)
+violinsheets That follows example #4. Think about rewriting it as "Maintaining a $1000 balance is necessary for not paying absurd bank fees." M is necessary for not F. ~F ⇒ M.
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
Why can't we have: If you pass a driver's test, then you can have a driver's license. If you do not pay absurd fees, then it means you have a balance of >= 1000.
"Passing a driver's test is required to have a driver's license." This states that passing a driver's test is a necessary precondition for having a driver's license, but that doesn't mean that there aren't other unknown preconditions for having a driver's license. If I say, "Getting a driver's license requires you to pass a driver's test and you must pass a substance abuse and traffic laws course" then the statement, "If you have a driver's license, you have passed a driver's test" because it is a necessary precondition for having a driver's license. However, the reciprocal, "If you have passed a driver's test, you have a driver's license" is not true because it has not shown that you have completed the second necessary precondition, which is passing a substance abuse and traffic laws course. "Well, the statement, 'If you have a driver's license, you have passed a driver's test' is not true because it also doesn't show that you have completed the second requirement." This is false because it starts at the assumption that you have a driver's license. If you have a driver's license then you have obviously completed both of the necessary preconditions, a driver's test being one of them. The statement is true because, even though it doesn't state the second requirement of getting a driver's license, it is still obviously true that you have fulfilled the first precondition for the driver's license.
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
Example 4. Why can it not be M => ~F? If you have a $1000 balance, then it must be the case that you do not pay absurd bank fees. Similar thing with example 5.
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
STATEMENT : The accused will be hanged only if the President rejects his plea for clemency. Which of the following is logically valid conclusion: 1) The President rejected his plea for clemency and so, the accused was hanged. 2) The President didn't reject his plea for clemency and so the accused was not hanged. 3) The accused was not hanged so the President must not have rejected his plea for clemency. 4) None of these.
I disagree with the notion that there is one single way to interpret these sentences. The real meaning of words is vague and undefined, one needs to simply feel the correct meaning. Who really is to say what is meant by a speaker, logically, when they express these sentences?
Example 1: P->(O&C) YAY! Example 2: H->V Oops you got me! Example 3: T->L DAMMIT! I guess this isn't true because even if you have passed the driver's test that does not necessarily mean that you have a driver's license. Example 4: M->~F Wouldn't this work as well?? If one has a 1,000 balance, then one doesn't have to pay absurd bank fees. Example 5: F->U Finally!
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
P => (O ^ C) H => V L => T ~F => M F => U After making a mistake in example 2, the rewriting of conditional statements into simple sentences started to make sense. Thank you for this MOOC! :)
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
P -> O^C L -> T -F _> M U -> F * Edit: Should be F -> U, because you can have U(nderstanding) of Logic from other sources than this course(F), but if you do this course(F) you have U(nderstanding)
I wanna see if I can clear some confusion. Some people are confused that this statement is not reversible. The statement can be edited to be reversible if you change "only if" to "if AND only if".
For example: "(You can play video games) IF AND ONLY IF (you've finished your homework)" is a reversible statement. This is because it secretly holds several statements in one. "if AND only if" combines the forward version of a statement with it's backward version.
SO! If you have "(You can play video games) IF (you've finished your homework)", you have V->H.
If you have "(You can play video games) ONLY IF (you've finished your homework)", you have H->V.
BUT! if you have "(You can play video games) IF AND ONLY IF (you've finished your homework)", you have the conjunction of both;
(V->H)^(H->V) which is the same as saying VH.
Hope I could help someone. It definitely helped me typing it down.
thanks :)
This comment helped me a lot thank you!
Thanks man
I was a bit confused by the examples, until you pointed out the difference between antecedent and consequent. Then it all made sense. Great video(s).
I honestly wish I had found your videos sooner. You make things easier to understand. Thank you!
+William Spaniel But Sir, In Example 2, both the statement and the converse are true
If you can play video games, than you must've done your HW
so V=>H
and if you did your HW, then you can play video games
V holds and H holds too, we express it with the notation VH
In the statement V, we're talking about the possibility of playing video games, it'll only be possible if you did your HW, but you don't actually have to play video games, but it's still true that it's possible if you'd done your HW
Please correct me if I'm wrong
If you did your homework, you can do whatever the fuck you want :P Not NECESSARILY play video games
+Gert van Immerzeel Hahahahaha thank you Sir for this comment, cheared me up in a stressful day xD
Take off your shoes and relax your socks
Gert Samson hahaaha
The only one that got me confused was #2.
Are they not reversible?
1. If you have finished your homework, you can play video games. (Because wouldn't finishing your homework automatically allow you to play video games, even if you don't?)
2. You can only play video games if your homework is finished.
So to me it seems like V H
Although I don't think it would work if you take out the "Can".
"wouldn't finishing your homework automatically won't allowed you to play games" Cause there's a IF only if homework is finished then game. If you convert that sentence into IF-THEN, then you'll come up with V=>H
think this way，it is equivalent to if you have not finished your homework ,then you can't play video games. ~H->~V , V->H
Just because you've finished your homework doesn't mean the electricity is running and the internet works.
But if nothing's stopping you then that includes the homework, which must therefore be 'done'
Hope more people have the chance to view the series of videos on logic! Thanks man! Its so helpful!!
I got all of these wrong until the end of the video, and then it all clicked, thanks man!
This is the first day of my master's econ studies. You saved me in my bachelor's, and you will save me once again. Thank you.
Great video, but could explain why it doesn't go the other way, like how License -> Driver test, but not Driver Test -> license, because you can pass the driving test and still not get it for failing vision test or have it rewoked.
Ex #1: P->(O^C) [right]
Ex #2: H->V [wrong]
Ex #3: T->L [wrong again]
Ex #4: M->(~F) [wrong again]
Ex #5: F->U [right, I redeemed myself]
You are very logical! You are my favorite teacher ever!
Thank you!
why cant we write this as " he maintains a 1000 dollar balance this implies he does not pay a negation fee."
For the example 2, I wrote ~H => ~V. Correct me if I'm wrong, but doesn't the sentence mean to say that if you don't finish your homework, you cannot play Video Games (as an order, which I have heard so many times btw).
When you hit lecture 18 (contraposition), you will see that ~H => ~V is identical to V => H!
Conditional? More like "conduit to wonderful" knowledge; thanks for all these amazing videos!
Just because the antecedent is false, it does not necessarily follow that the consequence is also false. I'll demonstrate this if anyone doubts this.
Question: Can you substitute "is required for" and "is necessary for"? Would the sentence change meaning if you do it?
1) P=>(O^C)
2) V=>H //I am learning programming and it's weird to me that logic should be express this way since it would need to be H=>V in a program.
3) L=>T //Ok this frustrates me since the sentences get flipped in this case. It seems to me it should be T=>L - If the driver's test is passed, then a driver's license can be had.
4) ~F=>M
5) U=>F
I agree with your second answer! logically it should be H => V / because you need to finish your HW first THEN you can play the game or whatever you want
"Passing a driver's test is required to have a driver's license." This states that passing a driver's test is a necessary precondition for having a driver's license, but that doesn't mean that there aren't other unknown preconditions for having a driver's license. If I say, "Getting a driver's license requires you to *pass a driver's test* and you must pass a substance abuse and traffic laws course" then the statement, "If you have a driver's license, you have passed a driver's test" because it is a necessary precondition for having a driver's license. However, the reciprocal, "If you have passed a driver's test, you have a driver's license" is not true because it has not shown that you have completed the second necessary precondition, which is passing a substance abuse and traffic laws course.
"Well, the statement, 'If you have a driver's license, you have passed a driver's test' is not true because it also doesn't show that you have completed the second requirement." This is false because it starts at the assumption that you have a driver's license. If you have a driver's license then you have obviously completed both of the necessary preconditions, a driver's test being one of them. The statement is true because, even though it doesn't state the second requirement of getting a driver's license, it is still obviously true that you have fulfilled the first precondition for the driver's license.
Example #1: P=>(O^C) // got it right!
Example #2: I think both "If you've finished your homework, then you can play video games." and "If you can play video games, then you've finished your homework." could work. Maybe both H=>V and V=>H are valid so it's some kind of reciprocal condition? Such as (H=>V)^(V=>H). // aaand I was wrong.
Example #3: "If one has a driver's license, the one passed the test" maybe? So L=>T // correct!
Example #4: "If one doesn't want to pay absurd bank fees, then it is necessary for one to mantain a $1,000 balance". I'm guessing the first statement has to be considered as a negative version of "one wants to pay absurd bank fees"; my answer is ~F=>M // correct =D.
Example #5: "If one has finished Game Theory 101, then one has a basic understanding of game theory". I'll go ahead and answer F=>U // I was right!
I also thought the 2nd example was a biconditional until i came across a comment that basically says:
-'Can' means that you have the OPTION to play video games
- But 'Can' only applies if you assume that the video game is working. The video game has to work in order for you to 'Can' play it
- So (H=>V)^(V=>H) is only true if you assume that the video game is working.
- Since it is not stated that the video game is working H=>V is false
- If you CAN play the video game, it necessarily means that it is working AND that you have finished your homework. therefore only V=>H is true
1. P => (O^C)
2. H => V
3. T => L
4. ~M => F
5. F => U
I rock at this.
This is my attempt at answering each examples:
Example 1: P ^ O v C
Example 2: H = V
Example 3: T = L
Example 4: M = F
Example 5: F = U
I guess I got most of them wrong except for the last one. I still keep on switching each of them up.
The operations team were fully staffed.
All the staff were Vulcans.
All Vulcans are logical.
Therefore all the operations team were Logical Operators.
If V & O than L
i have a question could i write these sentences (you can play video only if you have finished the home work ) with an exclusive or (A or ~B)or (~A or B) ?
The first example cannot be biconditional because obviously there are many adults that fit this description that are not the president of the United States. So it can only be written as P -> (O ^ C)
GOT IT.
Just because you've finished your homework doesn't mean the electricity is running and the internet works.
But if nothing's stopping you then that includes the homework, which must therefore be 'done' or rendered moot by the dog, which could be considered 'done' in a manner of speaking but i digress.
It's understood when V refers to the playing itself, but what if V refers to the possibility/ability of playing the videogames, i.e. "you CAN play videogames"?
Couldn't it ne written as "H=>V"?!
@@sahel600you cant because electricity is out
Also depends if can is meant as "have the means to" or "have the permission to".
I really dont get the statement at the end that
P -> Q = -P v Q
Looking at example 5 for instance, if finishing game theory 101-> understand game theory
This implies that one does not finish game theory OR they understand game theory??
What if they underatand game theory from an alternative means? Or what about if someone did finish game theory 101 but didnt underatand it. Does all of my confusion have to do witb the first proposition not being true itself?
For example #4, I think it would be F -> M. Here are my reasoning:
F: Not paying absurd bank fees
M: Maintaining a $1,000 balance
Therefore:
F -> M (If you are not paying absurd bank fees, then you are maintaining a $1,000 balance)
We cannot say ~F -> M because it means (If you ARE [negating the negative] paying absurd bank fees, then you ARE maintaining a $1,000 balance)
We can say ~F -> ~M because it means (If you ARE paying absurd bank fees, then you ARE NOT maintaining a $1,000 balance)
Please reply with regards to my correctness. Thanks :)
+Syed Ameed It looks like your mistake is identifying simple sentences. We can't use F to represent "you are not paying absurd bank fees" because "you are not paying absurd bank fees" is not a simple sentence. "You are paying absurd bank fees" is a simple sentence, though, and we can turn it into the antecedent of the conditional by adding a negation. Thus, ~F at the start.
William Spaniel Does the antecedent needs to be a simple sentence? I thought that we can use any statements, once it's closed and can be expressed as true or false.
+Syed Ameed The antecedent does not need to be a simple sentence. But single letters (like F) must be simple sentences. "I do not pay fees" = F isn't good because "I do not pay fees" is not a simple sentence. "I pay fees" is, however. So that's why we have ~F in the example.
In example #4 can it be M => ~f or ~M => F or ~F => M ?
You probably dont give a shit but does anyone know of a tool to get back into an instagram account??
I somehow lost the login password. I would love any tricks you can offer me
@Rex Caspian Instablaster =)
@Gunner Kayden Thanks so much for your reply. I got to the site on google and I'm waiting for the hacking stuff atm.
Seems to take quite some time so I will get back to you later when my account password hopefully is recovered.
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Thanks so much, you saved my account :D
@Rex Caspian Happy to help :)
is it fine to use an arrow with a single line, to mark the conditional operator, instead of two, as shown in the video?
1) P => O ^ C
2) V => H ..(my logic behind this is that if your are playing video game then you have already finished your homework so upon translating it I get if V is true then H is true... hope fully I am right)...YES
3) L =>T (If you have a driver's license then you passed a driver's test)
4) ~F => M ( if you are not paying absurd bank fees then you are maintaining a $1000 balance)
5) F => U ( If you finished GT 101 then you have a basic understanding of GT)
if the statement is
p-"I go to the beach whenever it is a sunny summer day"
then it's converse is
"if i go to the beach then it is a sunny summer day"
but i wanna know that if i write the converse of the statement p is-
"its a sunny summer day whenever i go to beach"
and the contrapositive is-
"its not a sunny summer day whenever i dont go to the beach"
will it be wrong? if yes then i wanna know why?
Ex1: P => (O . C)
Ex2: V => H
Ex3: L => T
Ex4: ~F => M
Ex5: U => F
why isnt it true for : if you passed the driver's test, then you have a driver's licence? T -> L?
The unfair answer is "because that's not what the statement said." A more helpful answer is passing a driver's test does not guarantee having a license---they might have failed the vision test or been ticketed for a DUI and had their license revoked.
Plz help me out!
passing a driver’s Test is required to have a driver’s License.
L=>T
Finishing game theory 101 is sufficient to have a basic Understanding of game theory.
F=>U
Grammatically both sentences are the same, but we convert them differently.
So how do we distinguish?
What seems to work is applying the following structure:
Left part is true => Right part is ALWAYS true
Then:
Conversion A: Left part (understanding game theory) => Right part (finishing game theory 101) is NOT always true, one might learn elsewhere
Conversion B: Left part (finishing game theory 101) => Right part (understanding game theory) is ALWAYS True, no contraction here
Thus: Conversion B is correct
What is the reason that would make me decide to flip the sentence around ?
So basically the first part is always the "if" part and the second part of the sentence is always the "then" part? (Except when you use 'required for'?)
In example #4 is it also correct to write
M => ~F
?
+Maderra -4 No, that would mean that maintaining a $1,000 balance ensures that you won't pay absurd bank fees. The English sentences leave open the possibility that one could have that much in the account but still pay absurd fees for some other reason.
@@Gametheory101 no it doesn't, the English statement says to avoid absurd BANK FEE'S (all encompassing term), it is necessary to maintain a $1,000 dollar balance. To void M=>~f, you should specify what fee you're avoiding, otherwise the statement covers all possible fee's.
the absurd complicates things, you could read it as expensive or unwarranted, but it is not a condition, it is a description of the bank fee's
It should also say a minimum of $1,000 balance; otherwise you could say that you get bank fee's for having over $1,000 in the account and who would bank at a place like that? :P
@@shitMountain "To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary *maintain a 1000 balance,* Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being *maintaining a 1000 balance.* Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of *maintaining a 1000 balance,* just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have *maintained a 1000 balance* still remains true."
isn't the backwards C horseshoe symbol also a superset symbol to denote that something (P) is the superset of another set (Q)?
can you please explain to me how "if p, then q" has the same logical meaning as "q unless ~p" ??? It's been driving me crazy. I can't understand it in terms of sentences and in terms of truth tables too
I think example #3 is incorrect. in writing if - then statement from a sentence, the subject remains the subject and the predicate also remains as the predicate.
"Passing a driver's test is required to have a driver's license." This states that passing a driver's test is a necessary precondition for having a driver's license, but that doesn't mean that there aren't other unknown preconditions for having a driver's license. If I say, "Getting a driver's license requires you to pass a driver's test and you must pass a substance abuse and traffic laws course" then the statement, "If you have a driver's license, you have passed a driver's test" because it is a necessary precondition for having a driver's license. However, the reciprocal, "If you have passed a driver's test, you have a driver's license" is not true because it has not shown that you have completed the second necessary precondition, which is passing a substance abuse and traffic laws course.
"Well, the statement, 'If you have a driver's license, you have passed a driver's test' is not true because it also doesn't show that you have completed the second requirement." This is false because it starts at the assumption that you have a driver's license. If you have a driver's license then you have obviously completed both of the necessary preconditions, a driver's test being one of them. The statement is true because, even though it doesn't state the second requirement of getting a driver's license, it is still obviously true that you have fulfilled the first precondition for the driver's license.
P => O ^ C
H => V [Correction: Reversed]
L => T
M => ~F [Correction: Got it backwards again]
U => F [Correction: Again Again backwards]
I guess I'll have to work on these things
(P -> (O^C
H -> V (Guess I got that wrong, but I used the same way: If you finished your homework, you can play videogames).
L -> T (reasoning being that if you have a license, you must have passed a driver's test, it must be true.)
M -> ~F (if you have maintained 1k bal, you will not pay absurd fees.) Guess I got that wrong too lol, probably because it's not always the case that when you maintain a 1k bal it must mean you didn't pay absurd fees. Maybe it's just your salary etc. Should work on it.
F -> U (wasn't too sure about this one, cause it isn't a sure outcome.)
Okay, I think example 4 is wrong. My book says "Q ⇒ P can also be read as P if Q and *P is necessary for Q*"
+violinsheets That follows example #4. Think about rewriting it as "Maintaining a $1000 balance is necessary for not paying absurd bank fees." M is necessary for not F. ~F ⇒ M.
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
Why can't we have:
If you pass a driver's test, then you can have a driver's license.
If you do not pay absurd fees, then it means you have a balance of >= 1000.
"Passing a driver's test is required to have a driver's license." This states that passing a driver's test is a necessary precondition for having a driver's license, but that doesn't mean that there aren't other unknown preconditions for having a driver's license. If I say, "Getting a driver's license requires you to pass a driver's test and you must pass a substance abuse and traffic laws course" then the statement, "If you have a driver's license, you have passed a driver's test" because it is a necessary precondition for having a driver's license. However, the reciprocal, "If you have passed a driver's test, you have a driver's license" is not true because it has not shown that you have completed the second necessary precondition, which is passing a substance abuse and traffic laws course.
"Well, the statement, 'If you have a driver's license, you have passed a driver's test' is not true because it also doesn't show that you have completed the second requirement." This is false because it starts at the assumption that you have a driver's license. If you have a driver's license then you have obviously completed both of the necessary preconditions, a driver's test being one of them. The statement is true because, even though it doesn't state the second requirement of getting a driver's license, it is still obviously true that you have fulfilled the first precondition for the driver's license.
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
1. P=>(O^C)
2. H=>V
3. L=>T
4. ~F=>M
5. U=>F
The first time I encounter them one was wrong. now the second time the last is good.
1. P => (O ^ C)
2. H => V wrong
3. T => L wrong
4. M => ~F wrong
5. F => U
H is P V is Q . P is followed by Q.
I love you guys, all you in the comments, for thou hast been pleasing to me!
Thank you so much!!
Example 4. Why can it not be M => ~F? If you have a $1000 balance, then it must be the case that you do not pay absurd bank fees. Similar thing with example 5.
The English statements allow for the possibility of paying fees for other reasons; M => ~F does not.
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
STATEMENT : The accused will be hanged only if the President rejects his plea for clemency.
Which of the following is logically valid conclusion:
1) The President rejected his plea for clemency and so, the accused was hanged.
2) The President didn't reject his plea for clemency and so the accused was not hanged.
3) The accused was not hanged so the President must not have rejected his plea for clemency.
4) None of these.
What is that v symbol at 7:47 mean exactly?
Leslie Fisher *or*
Not P or Q
Thanks
If P than O^C, If H=>V, L=>T, M=>~F (I didn't keep sentence order the same), F=>U
if-then: P=>(O^C) correct ☺
only if: H=>V wrong 😂
required: T=>L wrong 😂
necessary: ~F=>M correct ☺
sufficient: U=>F wrong 😂
#1 and #4 are my only correct answers
Why? I didn't give a counter argument for my own while answering lol.
H=>V for example 2
I disagree with the notion that there is one single way to interpret these sentences. The real meaning of words is vague and undefined, one needs to simply feel the correct meaning. Who really is to say what is meant by a speaker, logically, when they express these sentences?
Then it's the speaker's fault for logically misrepresenting what he meant to articulate, not logic's fault.
P => (O^C)
H => V
T => L
M => -F
F => U
This is confusing. It's hard for me to understand the proper order.
"If F than U" that is just as bad as "Not C".
I wonder if anyone has a theisis they have defended that contains (FU)NOT C.
if P then (O and C)
if H then V
If you homework finished, then play games...
Exemple #2 : H=>V
Example 1: P->(O&C) YAY!
Example 2: H->V Oops you got me!
Example 3: T->L DAMMIT! I guess this isn't true because even if you have passed the driver's test that does not necessarily mean that you have a driver's license.
Example 4: M->~F Wouldn't this work as well?? If one has a 1,000 balance, then one doesn't have to pay absurd bank fees.
Example 5: F->U Finally!
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
if P is true then O+C is true , but if P is false O+C is false
P=>(OvC)
Example 4 M=>F
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
P => (Q and R)
-F=>M
Ex 4 ~f=>m
P->OvC
P->(OvC)
^*
mayb "only if" means "and".... then V^H
negative...
P => (O ^ C)
H => V
L => T
~F => M
F => U
After making a mistake in example 2, the rewriting of conditional statements into simple sentences started to make sense. Thank you for this MOOC! :)
I bet you like that double line arrow, lmao!
Heck yeah, I do!
Example2 (Q=>P) Q: finish your homework,
P => ( O ^ C )
H => V - False
T => L - False
M => ~F - False
F => U
P=>(O'A)
P=>OvC
you had me at 5:29 XD. F => U
If P, Then O ^ C
P=>(O^C)
H=>V
L=>T
M=>~F
F=>U
This was more complicated, than I thought...
M=>F
P=>(O^C)
P =>( O & C)
H => V
Example 5 F=>U
P=>(O^C)
V=>H
L=>T
M=>-F
F=>U
I'm not sure I understand how some of these sentences are flipped but others aren't?
T=>L
V=>H
U => F
L -> T
How did I get here lol
L => T
got them all wrong lol
I would've flipped @4:25
"To not pay absurd bank fees, it is necessary to maintain a 1000 balance." It's saying that maintaining a 1000 balance is a necessary precondition for not paying absurd bank fees, but that doesn't mean that there are other unknown necessary preconditions for not paying a 1000 balance. I could say, "In order to avoid paying absurd bank fees, it is necessary maintain a 1000 balance, Keep multiple accounts at your bank, and Use only your bank's ATMs." Therefore, it you do not pay absurd bank fees, you have fulfilled all three necessary preconditions, one of them being maintaining a 1000 balance. Therefore, if you do not pay absurd bank fees you have maintained a 1000 balance as that is one of the three necessary preconditions for avoiding absurd bank fees. However, this does not mean that maintaining a 1000 balance makes you avoid absurd bank fees because you still need to fulfill the other two necessary preconditions for avoiding the absurd bank fees. However, if not paying the absurd fees necessitates the three preconditions, then you have obviously fulfilled the precondition of maintaining a 1000 balance, just that you have also fulfilled the other two preconditions. But the sentence, "If you have avoided paying absurd bank fees, you have maintained a 1000 balance still remains true." Therefore, ~F => M, but maintaining a 1000 balance still necessitates the fulfillment of the other two preconditions for M => ~F to be true.
P -> O^C
L -> T
-F _> M
U -> F * Edit: Should be F -> U, because you can have U(nderstanding) of Logic from other sources than this course(F), but if you do this course(F) you have U(nderstanding)
vape nash
P -> (O^C)
H -> V (wrong :( )
L -> T
~F -> M
U->F
P -> (O•C)
H -> V
T -> L
-F -> M
F -> U
Damn hahaha
V => H
L => T
V => H