This note is wroted to review note 01 TAT.

There are a very nonsensical statement is :"If pigs can fly ，than the horses can read".It's so funny,but in math this statement is perfectly natural in mathematics. but why?
(When an implication is stupidly true because the hypothesis is false, we
say that it is vacuously true.)

Here is the truth table for P => Q

P=>Q is always true if q isn't F. So P=>Q is logically equivalent to ¬P∨Q .
For this condition ,we write it as (P=>Q) ≡ (¬P∨Q).
If both P=>Q and Q=>P are true, then we say “P if and only if Q” (abbreviated “P iff Q”).

Here is another truth table which is bigger :

Quantifiers