p q ~q (p^~q) (p^~q)->q (p^~q)<->q
T T F F T F
T F T T F F
F T F F T F
F F T F T T
if q is true, then ~q is false.
if q is false, then ~q is true.
(p^~q) is only true if both p and ~q are true,otherwise it's false.
(p^~q)->q is only false if (p^~q) if True and q is false.
(p^!q)<->q is only True if both are True and if both are false. If they are mixed (TF or FT), then it's false.
A->B means that A implies B which states that "if A is true, then B is true".
A<->B means that A is equivalent to B which means that "if A is true, then B is true and if B is true, then A is true". This is also stated as "A is true if and only if B is true".
