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 example?

Question

Example : 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 such examples using direct proof?

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

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

Can someone explain what's the reason for the 3rd row of above truth tables' to be different?

Thanks!