Question

Can someone explain "if and only if"? If P and Q are both False, why is "P iff Q" True?

Answer 1

P if and only if Q, i.e. P iff Q, means that P and Q have the same truth value. Therefore, if P and Q both have the truth value "false", then P iff Q is true. P iff Q also means ((P implies Q) and (Q implies P)). Since the premise of each implication is false, the implications are both true and therefore P iff Q is true.

Answer 2

I don't understand the last part. P iff Q means implication both ways -- so can you help me understand how when they are are false it satisfies the implication both ways?

Answer 3

given P false and Q false
P->Q is true
also
Q->P is also true
thus
P->Q and Q->P is true
or in other words, P <-> Q is true