Question

What is the mathematical term for a statement that can be flipped and still remain true?
Example: A cat is a feline, and a feline is a cat.

AND/OR

What is the mathematical term for a statement that becomes false when flipped?
Example: A square is a rectangle, but a rectangle is not a square.

Answer 1

p->q is a conditional statement.
The truth table is
(T,T)=T
(T,F)=F
(F,T)=T
(T,F)=F

If p->q and q->p, then p<->q. It is a biconditional statement.
The truth table is:
(T,T)=T
(T,F)=F
(F,T)=F
(F,F)=F