Question 630377
your truth table is shown below:
<pre>
     p     q    ~q    (p^~q)    q <-> (p^~q)

     T     T     F      F           F
     T     F     T      T           F
     F     T     F      F           F
     F     F     T      F           T
</PRE>
you have 2 variables so there will be 2*2 = 4 rows
p and q have 4 possible variations.
they are TT TF FT FF
those options are shown in columns 1 and 2.
if q is true, then ~q is false.
if q is false, then ~q is true
that fact is shown in the third column.
(p^~q is true if both p and ~q are true, otherwise it is false.
that's shown in the fourth column.
q <-> (p^~q) is true if they both agree (either TT or FF).
Otherwise it is false.
<-> symbol is if and only if condition .
-> symbol is if then condition.
~ means not
T means true
F means false
here's a lesson written by yours truly a while ago.
it should still be valid.
<a href = "http://www.algebra.com/algebra/homework/Conjunction/THEO-2011-08-19.lesson" target = "_blank">http://www.algebra.com/algebra/homework/Conjunction/THEO-2011-08-19.lesson</a>
i'd give you more references but i ran out of time and have to go.