[Discrete Mathematics] Truth Tables Examples

[@Trevtutor]

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!

[@MathCuriousity]

Came across some confusing terms brother Trevor: I am wondering if “proof theoretic semantics” is same as “proof theory” and “model theoretic semantics” is same as “model theory” ? Thanks!

[@annalindborg4325]

I've just found this "classes". Soooo helpful for me to get the basics of discrete mathematics! Thank you!

[@HDitzzDH]

2:31 Pretty sure the fourth row is supposed to be false ( 0 -> 1 )

[@EvanGaoTV]

Nope, p-->q is only false if p is true AND q is false. Look at row 2, it's identical to row 4

[@HDitzzDH]

@@EvanGaoTV Nah, this is the problem with implication, true implies true, false implies false but false does imply true as well. However true does not imply false (If 1 is true and 0 is false).

[@EvanGaoTV]

@@HDitzzDH ah my bad, it is not identical to row 2. HOWEVER, 0-->1 is still true. The only case where the arrow is false is when 1-->0. With the whole sunscreen example, if it is sunny I will sunscreen. But, if it's not sunny, I can still wear sunscreen. I haven't broken my first promise, because I never said anything about if it ISN'T sunny

[@EvanGaoTV]

@@HDitzzDH you're thinking of biconditionality. Look at the previous video in the discrete math 1 playlist where he explains --> and how it is different from

[@mariahslittlelamb8049]

@@EvanGaoTV If a true statements implies something is false then it is always false. I agree with GZA.

[@monettedyar2837]

Thanks! Very helpful

[@eimaldorani]

[( A → B ) ∧ A] → B is a tautology However, instead of [( A → B ) ∧ A] we can not take B, isn't it? I mean [( A → B ) ∧ A] is not the same as B, isn't it? @03:16 to 03:23

[@Trevtutor]

It's logically equivalent, so yes it is the same.

[@akywongster]

I’ve been struggling so hard with this stuff but u make it look so easy omg ur brilliant

[@LR-wf8oq]

About 2:12 Guys, k->j = 1 if and only if k

[@KambeleChatroom]

thanks very much, i never understood these stuffs in class. love you so much Trev

[@mikaelsag]

is there an easy way to solve these problems without drawing out a truth table that i should know at this point, or is it normal do make truth tables for all of these problems

[@briananderson2283]

Why is: 'not P' = 1 + 'not(p or not q)= 0 in the 'Conditional' not = 0?

[@MrKB_SSJ2]

Exactly

[@Maroofgilani621]

@@MrKB_SSJ2 same question

[@Maroofgilani621]

i found the answer its not the not p =1 + 'not(p or not q) its if 'not(p or not q) then not p meaninig values of 'not(p or not q) are comparing with not p

[@liloupalomino8677]

3:05 You say you're simplifying. I would've thought [-(p || -q)->-p] would simplify to [(-p || q)->-p], but you say it simplifies to [(-p && q)->-p]. Can you explain why this is the case? Am I missing something?

[@karimalrawas3266]

you have stated in a previous video, that if a p=1 and q=0 in a conditional then p--->q = 0, yet here u put a 1, im i wrong???

[@Trevtutor]

Where did I put a 1 for that kind of statement in the video?

[@nahbruhwhat]

3:26?

[@mbarq2]

@2:30, You're reading it backwards, as [~p --> ~(pv~q)] where ~p=1 and ~(pv~q)=0, in that case yeah, it should be "0". It's not tho, it's: [~(pv~q) --> ~p], where where ~(pv~q)=0 and ~p=1, which yields "1".

[@ossahmadrezaazimikohnabi5108]

I wish I had a question 😂♥️ but thanks a lot for high quality teaching.

[@fancyAlex1993]

why is 2:31 true ? Shouldn't it be false ?

[@jonakatin]

i love this playlist buh can you recommend like a site or a book where I can get more activities

[@shegetsitdone]

Please what of word problems on this topic

[@khalidbornaparte6250]

Thank you man love you so much

[@hughlarsen9636]

helps so much great work!

[@sulemanahmed6770]

If I study Hard -- then I will pass == Satisfied with result :) If I study Hard -- then I don't pass == not satisfied with result :( If I don't study hard -- then I pass == F**k Yeah I am satisfied :D I I don't study hard -- then I don't pass == F**k it, I didn't study so I am satisfied with results :) i found this comment on another youtube video and it explains if then truth table. Hopefully this helps. If this is wrong let me know.

[@mohammednoural-rawabdeh5659]

you are an awesome person !!!!!!!

[@oleholeh9693]

No way, someone is watching this the same time with me. Absolutely agree with you that is cool explanation

[@johnfred975]

`~(p v~q)--> ~p can you explain more better cos i don't get the logic

[@_productivity__nill_1131]

I believe that was a mistake

[@ibrarsandhu1251]

you sir are a goat thanks so much

[@Mahanmarwat]

You are putting 1 0 on the P column but our teacher is putting 0 1 on the P column. What should I put? i.e P 1 0 Our teacher: P 0 1 I have learned that these are the binary equivalent of 0 and 1 and so on. i.e binary of 0 is 0 and binary of 1 is 1. So the first column starts from 0 and so on. So we should put first 0 then 1. Why are you doing the positive?

[@Trevtutor]

Most disciplines that use logic will write the positive lines first. A lot of older professors in computing science will start with 0, but this is all personal preference.

[@Mahanmarwat]

Thanks, But I going to stick to my professor method else he would not give me any number in a paper.

[@selvakumar-vd6oy]

admin ... can you explain the meaning of arrow ???

[@razeer1232]

Sth implies sth

[@thearchvile3560]

how old are you

[@MrKB_SSJ2]

3:27

[@MrKB_SSJ2]

0:00

[@neharikapuri3889]

for biconditionals the rule u said was "when am I lying to u, so for not(p v not q) for last one its like one is true and the other is false why is it true then. Its like u didn't put sunscreen but it was sunny or vice versa, either way on one side u r lying

[@EvanGaoTV]

Because it can be not sunny and I can still put on sunscreen for fun. I'm not lying to you that if it IS sunny, I would put on sunscreen. It isn't sunny, so nothing is out of bounds for me because I never promised you anything about if it ISN'T sunny.

[@EvanGaoTV]

Oh also -->is not a biconditional, a biconditional is

[@marinedestroyer7164]

is it just me or somebody else also find the truth tables to be extremely boring? not the explanation, but the topic itself for some reason

[@Dalia-zy9pg]

this is so bad he isnt explaining why it isnt 0 or 1