Thank you for this explanation of proofs. I have done them before in various math subjects, but never something like this. The assigned textbook in my class was difficult to follow along with and the associated assignments that were due while learning about proofs had almost nothing to do with them. This makes everything so much easier to understand.
I read this Book: Logic A vomplete interduction and i really just could not understand this! Thank, now i understand evrything (sry for my Bad englisch)
I will do how I think it is and see if is correct: I have to prove that D is true. D only appears in one premise and that premise is a disjunction. So the only way I see to prove D is with W being false. So first, then, to prove the veracity of D in fact I have to prove -W. So I see that -W appears in the second premise and because that is the only other premise in which W appears it has to be in that premise that W is proved as false. For that, -S has to be true because if not, there would be not a possible to know if -W is true or not, despite being the premise vacuously true. So I will look for S in other premise and I can see it in the first. Let's see if there is a way to prove that S is false then. I can see that in the first line If S then R. But in the last premise I see that R is denied. So there is a logically true formula that says "[[(P => Q) and -(Q)] => -P]". So in this case I can see that the antecedent of that formula is true since in the first line I have given as true that "IF S then R". And also I have in the fourth line given as true "-R". So the conjunction between those two is also true which gives as a result that then the antecedent of the logically true formula (known as the modus tollens or the way that denies by denying) is in this case true. Which allows me to reach the logical conclussion of "-P" that in this specific case will be "-S". Once I've got -S as a new premise I can go again to the second line premise and by means of the formula modus ponens I have the following: "[[(P=> Q) and P] => Q]". In this case if -S then -W is in the second line given as true and -S is given as true as a new premise that I've got as mentioned above with then implies that also the conjunction between those two will be true, which in turns gives that the antecedent of the formula is true which allows to logically arrive the conclussion: "-W". Now I'm almost done. I needed to get "-W" in order to be able prove the veracity of D. Once I have it I can apply the formula called disjunction introduction that is always true which is something like "[[(P or Q) and not (P)] => Q]". I have already in the third line the "W or D" part given as true and also have the "-W" part since I deduced it previously so the antecedent of the formula is true. If the antecedent of the disjunction introduction formula is true, then the consequent must be true since by definition in a true conditional proposition if the antecedent is true the same goes for the consequent, then I finally arrived to the fact that "D" is proven as a true.
I'm not sure if you meant to format your comment with a lot of text that is struck through, but if you could reply with more clear formatting, William or I might be able to offer advice.
@@PunmasterSTP I think I probably should've re-arranged -S -> -W as W -> S. Then I could've done something like: W --> S S --> R -R -W W or D -W D Would this be legit, and better than my initial attempt?
Ok sir using rules of inference is arbitrary am I right it does not have any specific condition that this rule of inference comes here after this prmise or usage of rules of inference is not governed by any rules am I correct sir 🙏
I don't think you have to use every premise, as long as your argument is sound. I think it would be like any other question where they might give you extraneous information to throw you off...
@@Gametheory101 Hello, do you have a hint for me how to prove ~A↔ B, ~B ↔ C, ~C ↔ A ╞ λ that? I already used the Df rule but I still cannot see how to show that an absurdity follows... Help would be much appreciated... Thank you!
god help me my professor isnt teaching jack shit and i have no idea what I'm doing I just took this course to help me with the last I'm running out of hair to rip out
I'm really sorry to hear that, and judging from the comments on here, a lot of professors aren't necessarily that great. How did the rest of your class go?
@@PunmasterSTP wow didnt think id get a reply to my comment! i did okay, i honestly learned more from youtube than i did through my professor. i cant believe i payed almost $4k for recycled content covid destroyed any chance of actually learning in university.
@@fezzes428 I'm sorry to hear about your school costs, but I'm glad that your class went okay! I like replying to old comments partly out of curiosity, but also because it has led to some cool conversations.
You're so much better of a teacher than my current prof!!! Thank you!
STLLR you can’t rewind your real life teacher :)
How did the rest of your class go?
Even during this COVID-19 pandemic - your videos make sense. Thanks William
Thank you for this explanation of proofs. I have done them before in various math subjects, but never something like this. The assigned textbook in my class was difficult to follow along with and the associated assignments that were due while learning about proofs had almost nothing to do with them. This makes everything so much easier to understand.
Literally everyone already said this but you saved me bro holy cow. Terrified for my exam on Wednesday but now I feel somewhat okay. Thanks
this stuff is miserable but i can’t help but love it
MODUS TOLLENS! Aw man I remember doing this back in the late 90s. Good times.
really really really helpful. you are a freaking godsend.
Thank you sir you have saved my grade!
Thanks for your videos!
If I pass my exam it'll be thanks to you
How did it go? Did you pass?
@@PunmasterSTP I did! This was for my Bachelor of Education. Thank you :)
@@Shapeplusform Awesome; I'm really glad to hear it!
BRO thank you someone finally made sense of this. lol you are a god send
I read this Book: Logic A vomplete interduction and i really just could not understand this! Thank, now i understand evrything (sry for my Bad englisch)
This is very helpful ,thank you so much😊
more please!
so helpful
In the formal system fitch we don't have Disjunctive Syllogism. How else would we get to the last step?
It is the same as mtp
I will do how I think it is and see if is correct:
I have to prove that D is true. D only appears in one premise and that premise is a disjunction. So the only way I see to prove D is with W being false. So first, then, to prove the veracity of D in fact I have to prove -W. So I see that -W appears in the second premise and because that is the only other premise in which W appears it has to be in that premise that W is proved as false. For that, -S has to be true because if not, there would be not a possible to know if -W is true or not, despite being the premise vacuously true. So I will look for S in other premise and I can see it in the first. Let's see if there is a way to prove that S is false then. I can see that in the first line If S then R. But in the last premise I see that R is denied. So there is a logically true formula that says "[[(P => Q) and -(Q)] => -P]". So in this case I can see that the antecedent of that formula is true since in the first line I have given as true that "IF S then R". And also I have in the fourth line given as true "-R". So the conjunction between those two is also true which gives as a result that then the antecedent of the logically true formula (known as the modus tollens or the way that denies by denying) is in this case true. Which allows me to reach the logical conclussion of "-P" that in this specific case will be "-S". Once I've got -S as a new premise I can go again to the second line premise and by means of the formula modus ponens I have the following: "[[(P=> Q) and P] => Q]". In this case if -S then -W is in the second line given as true and -S is given as true as a new premise that I've got as mentioned above with then implies that also the conjunction between those two will be true, which in turns gives that the antecedent of the formula is true which allows to logically arrive the conclussion: "-W". Now I'm almost done. I needed to get "-W" in order to be able prove the veracity of D. Once I have it I can apply the formula called disjunction introduction that is always true which is something like "[[(P or Q) and not (P)] => Q]". I have already in the third line the "W or D" part given as true and also have the "-W" part since I deduced it previously so the antecedent of the formula is true. If the antecedent of the disjunction introduction formula is true, then the consequent must be true since by definition in a true conditional proposition if the antecedent is true the same goes for the consequent, then I finally arrived to the fact that "D" is proven as a true.
I'm not sure if you meant to format your comment with a lot of text that is struck through, but if you could reply with more clear formatting, William or I might be able to offer advice.
@@PunmasterSTP It was unintended. I guess It's fixed now.
@@lea1822 Ah, gotcha! Did you have a question on a particular part of it, or do you feel good with the entire proof now?
@@PunmasterSTP I think I probably should've re-arranged -S -> -W as W -> S.
Then I could've done something like:
W --> S
S --> R
-R
-W
W or D
-W
D
Would this be legit, and better than my initial attempt?
I have a final primarily on this tomorrow. Let’s see if cramming works!
Well did it work
Yeah, how did your cramming and final go?
How did it go
now I won’t fail geometry tyyyy
How has geometry been going?
Am i the only one who laughed when he said "Now we have something that interacts with the D" at 4:15
King Joseph yes
yes
Funny hehe.
Ok sir using rules of inference is arbitrary am I right it does not have any specific condition that this rule of inference comes here after this prmise or usage of rules of inference is not governed by any rules am I correct sir 🙏
when you do a proof, do you have to use all the premises? If you can't use all the premises, is the proof wrong..?
I don't think you have to use every premise, as long as your argument is sound. I think it would be like any other question where they might give you extraneous information to throw you off...
I am getting slaughtered on one with 8 variables and no obvious route to take. fing sucks!
DeMorgans all the things.
@@Gametheory101 Hello, do you have a hint for me how to prove ~A↔ B, ~B ↔ C, ~C ↔ A ╞ λ that? I already used the Df rule but I still cannot see how to show that an absurdity follows... Help would be much appreciated... Thank you!
How did the rest of your class go?
My eardrums D:
?
god help me my professor isnt teaching jack shit and i have no idea what I'm doing I just took this course to help me with the last I'm running out of hair to rip out
I'm really sorry to hear that, and judging from the comments on here, a lot of professors aren't necessarily that great. How did the rest of your class go?
@@PunmasterSTP wow didnt think id get a reply to my comment! i did okay, i honestly learned more from youtube than i did through my professor. i cant believe i payed almost $4k for recycled content covid destroyed any chance of actually learning in university.
@@fezzes428 I'm sorry to hear about your school costs, but I'm glad that your class went okay! I like replying to old comments partly out of curiosity, but also because it has led to some cool conversations.