Question 479270
here's your truth table.
<pre>
       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
</pre>
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".