Propositional Logic Truth Trees (conditionals)

[@SuperBartles]

I love the logic videos! They are excellent. Hope there are more on the way. Subbed

[@MichaelSmith-sh7ns]

The first line of the truth table for P->Q is "True" also. So, why select the 3rd line of the truth table where P is False? Why use the so-called "vacuous truth" as the guide for decomposing the conational? I.e., why not use the first line in the truth table where P and Q are True? So that the decomposition becomes P & Q instead of not-P and Q. Does decomposing to P and Q lead to unexpected results in the "Truth Tree"?

[@victortruong2538]

You may not know it but you just saved the life of 80 French student who couldn't stay concentrated during logic class

[@rishikagupta7008]

hi! i think you have made a mistake while writing the alternative of negative (P bidirectional q) =0, the one on the left is correct, but the one on the right (i.e), not p and q should be true, precisely in 3:16 sec. here you said it is true but you wrote it as false. p.s I am really grateful for your videos. your explanations are very clear!

[@T-The-K]

Like the other person said, it seems there is a mistake at 3:16, i confirmed it with a truth table just to be sure. But another great video, just alot of rules that i need to let sink in since im binge watching these in short term.

[@naiko1744]

Not( P Q) = 1 when ( P Q) = 0 P Q = 0 when they have different values There's two ways for P and Q to have different values: P is 1 and Q is 0 P is 0 and Q is 1 We can write both cases in 2 ways each: - P is 1 and Q is 0: 1. P = 1, not Q = 1 2. not P = 0, Q = 0 - P is 0 and Q is 1: 1. P = 0, not Q = 0, 2. not P = 1, Q = 1 The mistake of the video was writing two examples from the same case, and not one example for each case.

[@nitishgautam5728]

0:57 this is incomplete information that p Implies a will only be true when p equals 0 or q equals 1 , we have seen that for p =1 also we had 1 in truth table so Correct reasoning would p Implies a is only true when double negation p Implies a is true , now - - (p implies q ) is true if - (p implies q ) is false and we know this will happen when p = 1 AND q =0 .... So now in truth tree we write proposition in true forms so final expression will look like - (p AND -q) now finally if we simplify this we get by law -p OR q.

[@Trevtutor]

“We have also seen that for p=1 also we had 1 in truth table so” Yes, because Q=1, which satisfies the condition of P=0 or Q=1.