Check out my new course in Propositional Logic: trevtutor.com/p/master-discrete-mathematics-propositional-logic It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!
Thank you a lot, you saved me. My college professor has a lot of knowledge but he likes to make the logic course overly complicated and abstract, not teaching anything at all. You have saved my course.
(To my knowledge) Anyone who may need this in the future: Addition can be used to make a statement bigger. I saw a great example where it's explained like: Jackie likes pancakes (Premise). Use addition to say Jackie likes pancakes OR dirt. It doesn't matter that Jackie doesn't like dirt, because the Jackie likes pancakes is true. He is adding NOT L to NOT S so that we can use modus ponens to prove that "R or F". NOT S or NOT L --> R or F (this is from line 6/7) NOT S or NOT L (Got this from adding NOT L to the end of line 4, NOT S. Doesn't matter if NOT L is true or not. It's an or statement) Therefore, R or F must be true. Word example: if Jackie doesnt like candy or doesnt like pears, then she likes apples or chips. Jackie doesnt like candy or doesnt like pears. Therefore, jackie likes apples or chips.
Thank you TrevTutor I believe you really do help a lot of people that previously did not have the opportunity to study further due to financial issues or time constraints etc.
Hi, you're an amazing teacher. Without you my discrete structures course would have been a complete nightmare. I have liked, subscribed as well as shared it with my whole Discrete class. :D Keep up the good work, sir. :)
The grate work when you help people forever . The grate work sir done its since 4 year people are still using this video. 🙏🏻😍😇 and have a easy method .
Thank god for UA-cam and good people like you. My professor runs through this stuff in about 2 min and then just expects us to know how to do proofs like the last one you did.
I feel like text books skip the parts that make a lot of rules in math make so much more sense when mentioned by a person. I read all of the rules from mine and was just like "...." This made them make more sense by adding a few words the books left out lol.
Because I wanted to use Modus Ponens to get to the consequent and finish the proof. The rules never tell us what to do, but they tell us what we can do. We still have to keep in mind where we're trying to go and what we can do to get there when we do these proofs.
Mia Q, if you use the conditional law on step 6 instead of the DeMorgans law, then on step 7 use the DeMorgans and Double Negation, you will get the following result: (S AND L) OR (R AND F). Then you can apply the Disjunctive Syllogysm from step 4 and 7 to get (R AND F). From there you use the Addition Law and get R. This is not the approach TrevTutor used but I thought it might be good to see two examples to grasp the addition.
Thank you so much for this video and the whole course! My teacher cannot hope to be as good at teaching as you are. Do you think it's possible to do the last problem without the logic laws and only the rules of inference?
TheTrevTutor Just wanted to jump on the thank you bandwagon! Great work man, you have really helped me out in my Discrete Structures course. Thank you so so much :) I hope you're profiting off this service in some way or another if that is your ultimate goal. Anyways, kudos.
i used fewer steps in the last exercise: ¬s is true so s ^ L = F which would make ¬R v ¬F also F for premise 1 to be true which means both ¬R and ¬F are False which makes R true. i'm not sure what specific rules would apply for each step though
This was a great introduction and I followed it well up until that second example which had me totally flummoxed, though I can see how you got there. Thx for sharing.
I know you posted this a while ago but I want to thank you anyhow. This reply helped me check my own work and also gave a really great example of how to post a clear to read proof inside a youtube comment. I wasn't sure how to communicate what i was writing on my notebook when typing things out and this reply really helped clear things up.
@@nielsnielsen1360. I'm glad to read that! :D It's really cool when you receive positive feedback on something you didn't even remember you had written xD; also, I get to see my past comments and feel as if they were mine but from someone else.
what I did was this: Modus Tollens like you started then I took ~S, and used it to show that (S and L) is wrong therefore we have ~(S and L) [(~R or ~F) => (S and L)] and ~(S and L) therefore ~(~R or ~F) therefore R and F therefore F therefore R
For those of u who didn't undertsand line 8, he took line 4 "~s" and applied addition law to that. this will get us (~s or~l). then applying this to line 7 we get line 9.
would it be a valid step to go from ~ (S^L) --> (R^F) to ~S --> (R^F) & ~L --> (R^F) using ^E/Simplification as the justification? Or is that illegal (and if it's illegal, why?)
In the second exercise, I used not(s^l) for step 5, allowing me to reach the conclusion in 8 lines instead of 10. If you already have not(s), then you automatically have not(s^l), yes? Is there a name for that rule, or is it just the definition of and?
not(s^l) isn’t logically equivalent to not(s) not(s^l) is logically equivalent to not(s) [or] not(l) That’s by DeMorgan’s Laws. That was a good try though definitely insightful
At 11:30 , can you please explain the addition step? For addition to work, you must have ~S and ~L alone, but only ~S was alone so where did the ~L come from? Thank you.
This is a really great video and I'm glad I watched it; but I feel the premises should be in lower case, since in the last example I thought the F is a premise instead of False.
Can we use Simplification Rule in place or we must have a separate premise to use it? For expample: (not R or not F) then (S and L), are we able to convert this to (not R or not F) then S?
A premise is needed. When you don't have the premises, you use the simplification because you are treating all the lines of the truth table. When we use rules of inference, we are only interested in one line of the truth table, the line which obey the premises.
So are we just assuming every proposition is true when doing these proofs? My book didn’t explain this at all, the video wasn’t entirely clear either but did help. My mind is trying to consider every possible value for each prop and it’s pretty overwhelming and not well explained
I guess it would be easier to understand inference as the process of elimination of possibilities in truth tables. The way I learn inference is by using truth table.
Fengbeiling Wang assuming you mean simplification by “Domination Law,” you could conclude F from R ^ F. But that’s not really useful for our problem here since the problem asks us to conclude with R and not F
that was awesome. points well explained and easily understood. Thanks so much. would you kindly help me proove the first absorption law using truth tables. Thanks in advance
no. Modus Tollens is applied when you have propositions in the form: (S->T)^(~T) which implies (~S) (essentially contrapositive reasoning applied to Modus Ponens). With the propositions you have supplied, I am pretty sure that there is no logical inference that can be made.
Just curious - I am teaching a homeschool class and they are 8th graders. We are do intermediate logic now and they are not grasping it well. How young is too young to be working with this stuff?
I don't know if there's an age that I'd recommend. I think it's more about mathematical maturity and experience. Rules of inference might need a lot of real life examples to be understood well, and it also might not be a bad idea to introduce logic puzzles first and then move onto actual mathematical logic.
Check out my new course in Propositional Logic: trevtutor.com/p/master-discrete-mathematics-propositional-logic
It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!
0-1000 from the first example to the second example
i swear......we need more examples...any suggestion videos?
@@andremwaura1684 "discrete math examples" on UA-cam
Thank you a lot, you saved me. My college professor has a lot of knowledge but he likes to make the logic course overly complicated and abstract, not teaching anything at all. You have saved my course.
Same here, we are the ones to find the solution to the dilemmas.
This really solidified things for me. I was confused about this part in class, thank you!
This is golden! Thanks for mentioning the NAMES of the methods, my teacher just calls them "figure 1.11 lemma 12" and so on. So confusing.
Hi, I am confused about when we can use addition (as in example 2 for step 8). Why do we introduce addition and when do we use it in general?
(To my knowledge) Anyone who may need this in the future: Addition can be used to make a statement bigger. I saw a great example where it's explained like: Jackie likes pancakes (Premise). Use addition to say Jackie likes pancakes OR dirt. It doesn't matter that Jackie doesn't like dirt, because the Jackie likes pancakes is true.
He is adding NOT L to NOT S so that we can use modus ponens to prove that "R or F".
NOT S or NOT L --> R or F (this is from line 6/7)
NOT S or NOT L (Got this from adding NOT L to the end of line 4, NOT S. Doesn't matter if NOT L is true or not. It's an or statement)
Therefore, R or F must be true.
Word example:
if Jackie doesnt like candy or doesnt like pears, then she likes apples or chips.
Jackie doesnt like candy or doesnt like pears.
Therefore, jackie likes apples or chips.
Would it not be "Jackie likes apples AND chips instead of OR? I dont know if I misunderstood. @@kaminvdi
I hope this video will help me for our exams tomorrow. Wish me luck guys
I too have exam of logic tomorrow
good luck to us
Jorge Martinez, II I have it this Friday lol
tommorow
@@gpakkol6682it turned out well
mine begin in 3 weeks from today
You're a beast.
Can you please make a video about turning formulas into DNF or CNF (not necessarily full) without truth tables ?
u found one yet?
@@مانجاه he is properly died by now if u want a website that can turn DNF to CNF or CNF TO DNF. massage me
@@basam1459 ya send me the link here
I'm gonna need you to make the way you wrote "contrapositive" into a font because it looks so satisfying.
contraceptive is a better word :P
Thank you TrevTutor I believe you really do help a lot of people that previously did not have the opportunity to study further due to financial issues or time constraints etc.
"Yeah, it's not always super straightforward "
Hey, woah, easy with the big guns.. ouch.
Really awesome lecture, tho, thanks man..
You're an amazing teacher!
With such a soothing voice :)
I second this
I third this
🤭🤭
I fourth this
TrevTutor saving my DM univerisity module 6 years before it started! THANKS SO MUCH ! It makes so much more sense when explained like this ♥
Hi, you're an amazing teacher. Without you my discrete structures course would have been a complete nightmare.
I have liked, subscribed as well as shared it with my whole Discrete class. :D
Keep up the good work, sir. :)
انت كنت aast ?
The grate work when you help people forever .
The grate work sir done its since 4 year people are still using this video.
🙏🏻😍😇 and have a easy method .
I LOVE YOU SENSEI 😍😍😍 this is the easiest to understand explanation
this video is great, really helped me out. loved the hard example at the end and how simple you make it.
Could you please provide an additional sheet of Q&A for this video. It was very interesting and would love to have some practice with more examples
Thank god for UA-cam and good people like you. My professor runs through this stuff in about 2 min and then just expects us to know how to do proofs like the last one you did.
I feel like text books skip the parts that make a lot of rules in math make so much more sense when mentioned by a person. I read all of the rules from mine and was just like "...."
This made them make more sense by adding a few words the books left out lol.
You are the best tutor I have ever seen, Good Work, Thanks indeed and wish you a happy wonderful life!
I didn't understand step 8 where you used 4 and addition, how did you know that you need an addition and why you chose "not S" with "not L"?
Because I wanted to use Modus Ponens to get to the consequent and finish the proof. The rules never tell us what to do, but they tell us what we can do. We still have to keep in mind where we're trying to go and what we can do to get there when we do these proofs.
Mia Q, if you use the conditional law on step 6 instead of the DeMorgans law, then on step 7 use the DeMorgans and Double Negation, you will get the following result: (S AND L) OR (R AND F). Then you can apply the Disjunctive Syllogysm from step 4 and 7 to get (R AND F). From there you use the Addition Law and get R. This is not the approach TrevTutor used but I thought it might be good to see two examples to grasp the addition.
Johan Rönkkö *McCarran
you're right johan ronkko (that's not confusing)
Johan Rönkkö You made some mistakes. :) From (R AND F), you don't get R with the Addition Law, also there was some other mistakes.
You're the best. I almost gave up on this math class. Thanks to you. I am starting to understand the concepts.
for the last question you can also to this type of process. 1.) 2,3,MTT 2.) 1, result of 1.), MTT. 3.) De Morgans, 4.) Simplification. That's it.
Thanks for much for this. Do you have some material for rules of inference for quantified statements
Thank you so much for this video and the whole course! My teacher cannot hope to be as good at teaching as you are.
Do you think it's possible to do the last problem without the logic laws and only the rules of inference?
Yes, but we'd need a few more rules to make it work.
TheTrevTutor Just wanted to jump on the thank you bandwagon!
Great work man, you have really helped me out in my Discrete Structures course. Thank you so so much :)
I hope you're profiting off this service in some way or another if that is your ultimate goal.
Anyways, kudos.
i used fewer steps in the last exercise: ¬s is true so s ^ L = F which would make ¬R v ¬F also F for premise 1 to be true which means both ¬R and ¬F are False which makes R true. i'm not sure what specific rules would apply for each step though
amazingly detailed! cleared all my confusions. Thank you so much!
This was a great introduction and I followed it well up until that second example which had me totally flummoxed, though I can see how you got there. Thx for sharing.
Thank you for your explanation. It is easy to understand.
Here's another, slightly longer, proof of the second example:
1. (ㄱR∨ㄱF)→(S∧L) Premise
2. S → T Premise
3. ㄱT ∴ R Premise & Conclusion
4. ㄱS 2,3 MT
5. S∧L assumption for Indirect Proof (Reductio)
6. S 5 Simplification
7. S∧ㄱS 6, 4 Conjunction
8. ㄱ(S∧L) 5-7 Indirect Proof (Reductio)
9. ㄱ(ㄱR∨ㄱF) 8,1 MT
10. ㄱㄱR∧ㄱㄱF 9 DeM
11. R∧F 10 DN
12. R 11 Simplification
I know you posted this a while ago but I want to thank you anyhow. This reply helped me check my own work and also gave a really great example of how to post a clear to read proof inside a youtube comment. I wasn't sure how to communicate what i was writing on my notebook when typing things out and this reply really helped clear things up.
@@nielsnielsen1360. I'm glad to read that! :D It's really cool when you receive positive feedback on something you didn't even remember you had written xD; also, I get to see my past comments and feel as if they were mine but from someone else.
can you help me with my assignment
DO you have a video for inference rules for quantifiers ?
Very nice video with a clear explanation. I'm curious about the app you use for this "whiteboard". Much clearer than what I have.
this was really helpful.....but could you make an examples video for these rules of inference?
Finally, it took four separate explanations for me to figure it out. Thanks!
thanks. you explained it very well... really gonna help me for tomorrow's test!
what I did was this:
Modus Tollens like you started
then I took ~S, and used it to show that (S and L) is wrong
therefore we have ~(S and L)
[(~R or ~F) => (S and L)] and ~(S and L)
therefore ~(~R or ~F)
therefore R and F
therefore F
therefore R
For those of u who didn't undertsand line 8,
he took line 4 "~s" and applied addition law to that. this will get us (~s or~l). then applying this to line 7 we get line 9.
But why use l instead of any letters
would it be a valid step to go from ~ (S^L) --> (R^F) to ~S --> (R^F) & ~L --> (R^F) using ^E/Simplification as the justification? Or is that illegal (and if it's illegal, why?)
Thanks, where can i find a video about imply introduction
In the second exercise, I used not(s^l) for step 5, allowing me to reach the conclusion in 8 lines instead of 10. If you already have not(s), then you automatically have not(s^l), yes?
Is there a name for that rule, or is it just the definition of and?
not(s^l) isn’t logically equivalent to not(s)
not(s^l) is logically equivalent to not(s) [or] not(l)
That’s by DeMorgan’s Laws. That was a good try though definitely insightful
Reviewing for the test later. Last minute!
Hello, in simplification if the premise are ~p ^ ~q, then what is the answer ? is it ~p ? thank you so much.
YOU are an absolute friccing legend, thanks for this
Have a problem with example 2 in step 8. Where are disappeared R^F?. Because additional is when you have one leter P after you get it P or Q.
This is the very video if everyone watches and masters the world will be a much better place.
Thanks for making it so easy to understand!
How do you know that its a tautology though unless it says so or if you use a truth table to prove it...
At 11:30 , can you please explain the addition step? For addition to work, you must have ~S and ~L alone, but only ~S was alone so where did the ~L come from?
Thank you.
he is referring to step 4 not 7
I greatly appreciate all the you're doing to help teach those who come asking for help.... but DAM. This is still not enough.
Thanks watching this a few times it starts to make more sense :D
For number 5, could you use MTT on 1 and 4 as well to get R and F?
This is a really great video and I'm glad I watched it; but I feel the premises should be in lower case, since in the last example I thought the F is a premise instead of False.
Tq sir
I can understand only rules not problems plz upload more problems....
Can we use Simplification Rule in place or we must have a separate premise to use it? For expample:
(not R or not F) then (S and L), are we able to convert this to (not R or not F) then S?
A premise is needed. When you don't have the premises, you use the simplification because you are treating all the lines of the truth table. When we use rules of inference, we are only interested in one line of the truth table, the line which obey the premises.
So are we just assuming every proposition is true when doing these proofs? My book didn’t explain this at all, the video wasn’t entirely clear either but did help. My mind is trying to consider every possible value for each prop and it’s pretty overwhelming and not well explained
Very helpful, thank you so much.
Thank you very much. It help us very much
Awesome video man, by chance the examples you went over were in my tutorial today and it all makes sense now
so how about this problem? (p->q)^(pv~r)^(~r->s)^~s->q?
broo tysm, i'll def be coming back to this!
(Best of all time )discrete math videos!!! keep going!!!
Thank you for making this video
I guess it would be easier to understand inference as the process of elimination of possibilities in truth tables. The way I learn inference is by using truth table.
The last example
We can use 1,4,Mtt
And that give us ~(~r OR ~f)
Did it work?
Then use the simplification
In the last example, why isn't R and F considered F using Domination Law? I am confused. Thanks for answering!
Fengbeiling Wang assuming you mean simplification by “Domination Law,” you could conclude F from R ^ F. But that’s not really useful for our problem here since the problem asks us to conclude with R and not F
that was awesome. points well explained and easily understood. Thanks so much. would you kindly help me proove the first absorption law using truth tables. Thanks in advance
Check it is valid or invalid??
If the two sides of the triangle are equal then opposite angles are not equal .Therefore opposite angles are not equal
12:15 did you guys saw he wrote simp
bruh
@@Jjaro7515 i was kinda drunk lol
not really
in the last example, if we would entail L would we write L as an answer?
simply amazing! Thank you!
@TheTrevTutor
What would be the process to solve the following:
1) e V a
2) e → ¬p
3) ¬p
∴ a
Oh man, it's been a year. But it would probably have been 4. e (2,3 MP) 5. a (1,4 SIMP) or something similar.
Hi @TheTrevTutor, How can from notS in line 4 become (notS or notL) with an addition rules?, i still don't get it :'(
Take S implies T and ~s then apply modus tolens then ~T is the result, Is this correct ?
no. Modus Tollens is applied when you have propositions in the form: (S->T)^(~T) which implies (~S) (essentially contrapositive reasoning applied to Modus Ponens). With the propositions you have supplied, I am pretty sure that there is no logical inference that can be made.
can you use simplification in A v B to get only A?
Excellent explanation bro!!! Loved it.
towards the end of the last problem couldn't you use MTT again? like not R implies not S, S, therefore R??
Can I ask about when to use contrapositive to reason?
My lecturer requires only the use of inferences not the laws of logic is there a way to do the last question using laws of logic?
Thank you, God bless. 😊
Nice video, thanks alot
awesome introduction to this topic!
[ (pvq)^q›~p] is this disjunctive syllogism?
Automatic sub.... Thanks man you really came through clutch with this video.
Hope this helps me in my exam too
good way of teaching
If its pvq can we use addition rule and write it as p? Or is it only true for the other way
Only p -> pvq.
If you want to do pvq ->p, then you must show p->p and q->p.
i don’t understand logic when it comes to proofs. i suck at logical equivalences and rules of inference proofs. I NEED ADVICE!!!!!!
hi can someone explain how did the addition part happen in the last example :
Can you make a video doing some experience of this ?
Just curious - I am teaching a homeschool class and they are 8th graders. We are do intermediate logic now and they are not grasping it well. How young is too young to be working with this stuff?
I don't know if there's an age that I'd recommend. I think it's more about mathematical maturity and experience. Rules of inference might need a lot of real life examples to be understood well, and it also might not be a bad idea to introduce logic puzzles first and then move onto actual mathematical logic.
bro am not able to get the problems done . Will practising the laws improve the way i solve problems
thank you very much. got it
please.. I need help with
1. p∧q→¬r
2. p∨¬q
3. ¬q→p
∴¬r
How can we start to solve it?
In what year do y'all study this?
Me in 2nd year cse
can you add an variable with negation???
u r the best
i hope this video will help me for the exam after 2 hours.
I am hopeless dude
How was your exam? 😣
I can't understand it at all. I'm hopeless, too.
what is life man
@@saras2367 I dropped the course, hopfully i will take it in another noncorona semester.😂
Thanks a lot
Nice explanation 😊