Laws Of Logical Equivalence

This is a video on 10 laws of logical equivalence and 2 important statements guaranteed to solve any tautology, logical equivalence, and the truth table.
**NOTE: I made a mistake in this video, the second bi-conditional should be
1) p↔q≡¬p↔¬q
or
2) ¬(p↔q)≡p↔¬q
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More videos on Logical Equivalence:
(0) Logical Equivalence: • Prove Logical Equivale...
(1) Tautology: • Truth Table Tautology ...
(2) Tautology: • Prove the Logical Expr...
(3) Contradiction: • Logical Equivalence Co...
(4) Laws: • Laws Of Logical Equiva...
Play List of Logical Equivalence / Proposition Logic:
• Logical Equivalence Co...
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[@realNaniByte]

very helpful to have them all collected in one place

[@zack-ni3ru]

sir how to prove these laws using truth table. specially identity laws..

[@jesserosenthal9606]

Hello Randerson can you tell me how do I know what logical statement to start when showing equivalence? When I look at all the laws I don't know what's the best way to start a lot f times.

[@randerson112358]

Hi, I would start with the logical equivalence statement that is given for example in my video: th-cam.com/video/Wyd-PLf2mc0/w-d-xo.html
I have to prove (p and -q) or q = (p or q)
So I try and simplify the equation:
by substituting p3 for ( p1 and -q1) and substituted q3 for q2 (NOTE: I am only using the numbers to differentiate the variables aka q and p)
Then I look to see if there is a law using only the variables that I used aka p and q and there is, the commutative law. Which would change the original equation from (p and -q) or q to q or (p and -q).
Then I continue with this method, I look for a law that looks similar to my current equation, in this case the distributive law looks similar. So this will change our current equation from q or (p and -q) to (q or p) and (q or -q)
Then we see that we have something that looks like our answer ' (p or q) ' except it has 'and (q or -q)' so we must find a way to get rid of the 'and (q or -q)' . There happens to be another law called negation that will change (q or -q) to True or 'T'.
So now our equation looks like (p or q ) and T, so now we must still get rid of the T, and I see that there is another law called domination, where I can substitute (p or q) for p such that we get p and T, then using the domination law we can get rid of the T, since (p and T) = p . So our equation becomes just (p or q).
I hope that helps a little bit;
randerson112358

[@jesserosenthal9606]

Thank you much man.

[@zsefvgyjmko1973]

2nd biconditonal statement
isnt it supposed to be
p=q == notp = notq

[@randerson112358]

+ASHIQ thanks you are correct, it seems I have made a mistake there it should be either:
1) p↔q≡¬p↔¬q
or
2) ¬(p↔q)≡p↔¬q
Thanks Again!
randerson112358

[@gaiseric9518]

Why do 95% of math professors not even provide these laws at all? I'm very grateful for these videos, but I also find a newfound hatred for my academic college whenever I discover that something that had caused so much mental anguish was caused simply because they didn't provide me with these laws when they should have and just told me to go solve proofs without them.

[@moizkhalid2714]

sir you did not explain any thing...you just read the laws... :(

[@moizkhalid2714]

sir you did not explain any thing...you read the laws... :(

[@randerson112358]

Hi moiz,
I used this video as a reference for my other videos on Logical Equivalence so that viewers could easily watch/learn about the different laws, and not to prove each of the laws, however you could use a truth table to prove these laws of equivalence if that is the explanation you are looking for.
Thanks for watching;
randerson112358

[@gaiseric9518]

Leagues above my professor, he didn't even give us the laws.

[@rizwanmehdi1734]

sir please question understand us in urdu

[@oldmate4140]

Nice chart, but you really didn't explain anything.

[@randerson112358]

Hi,
Thanks! I have many videos on logical equivalence. This video was created as a supplement for some of them. The videos are below. Let me know if this is what you are looking for.
More videos on Logical Equivalence:
(0) Logical Equivalence: th-cam.com/video/Wyd-PLf2mc0/w-d-xo.html
(1) Tautology: th-cam.com/video/N8yhE1GaaQc/w-d-xo.html
(2) Tautology: www.youtube.com/watch?v=okZcT...
(3) Contradiction: www.youtube.com/watch?v=YXSYB...
-randerson112358