Can someone explain me why the truth table of p-->q, given that p and q are any two propositions, does not agree with the truth values of the direct proof of the following?

Question

I know that the general truth table of p-->q takes following form :

p , q , p-->q

1) T , T , T
2) T , F , F
3) F , T , T
4) F , F , T

Prove that if x is an even integer, then x^2 is also an even integer using direct proof :

Let a,b denote x is an even integer and x^2 is an even integer. We usually take a-->b to prove as above example.

So the above example's truth table takes following form :

a , b , a-->b
1) T , T , T
2) T , F , F
3) F , T , F
4) F , F , T

Can someone explain what's the reason for the 3rd of both above truth tables' to different.

Can someone explain?

Thanks a lot!

Answer 1

Is this one question or multiple questions in a single post? It's hard to tell where one possibly rhetorical question ends and the next one begins.

It might help to re-post this question with specific focus on a particular question that you need assistance with.