SOLUTION: I have done a truth table below and i need someone to check it for me. I am not sure if I have it set up right. The ~q and --> has me a little confussed.. ~q-->(p^q) p q q

The truth table contains only 4 lines, not 8.
So first you need to learn the formula for the number of lines
in a truth table.  That formula is



When there is one letter as in p-->(~p^p), there are 
only 21 or 2 lines in the truth table.

When there are 2 letters as in ~pV(~q^p), there are 2² or 4 
lines in the truth table.
 
When there are 3 letters as in pV(q^r), there are 2³ or
8 lines in the truth table.

Your statement

~q-->(p^q)

has only 2 letters, p and q, so you should only have 
2² or 4 lines:

We break ~q-->(p^q) down into its five parts

(1) p
(2) q
(3) ~q
(4) (p^q)
(5) ~q-->(p^q)

The first parts (1) and (2) are the letters.

Then we can get the truth value for (3) ~q by looking 
at (2) the truth value for q

Then (4) we can get the truth value for p^q by looking 
at (1) and (2), the truth values for p and q  

Finally we can get the truth value for the whole
expression by looking at (3) and (4), the truth values
for ~q and (p^q).

So we make five columns on the truth tables.
(you can leave out the line numbers if you like)


line# p  q  -q  (p^q)  ~q-->(p^q)
_________________________________
  1
  2
  3
  4

We start out putting TTFF under p and TFTF 
under q:

line# p  q  -q  (p^q)  ~q-->(p^q)
_________________________________
  1   T  T
  2   T  F
  3   F  T
  4   F  F

Since the list under q is TFTF we just put the 
opposite, FTFT, under ~q:

line# p  q  -q  (p^q)  ~q-->(p^q)
_________________________________
  1   T  T   F
  2   T  F   T 
  3   F  T   F
  4   F  F   T

Under the (p^q) we put T on the line that has p and q 
both as T and we put F otherwise.  The only line that gets 
a T is line# 1 because that's the only line in 
which p and q both have T's.  So under the (p^q) we put TFFF

line# p  q  -q  (p^q)  ~q-->(p^q)
_________________________________
  1   T  T   F    T        
  2   T  F   T    F       
  3   F  T   F    F       
  4   F  F   T    F       

Finally under the conditional --> we put F only on lines
when there is a T under whats on the left of -->, which is
~q and an F under what's on the right of the -->, which is
(p^q) . That is the case in lines #2 and #4, so under the
--> we put TFTF in the last column: 

line# p  q  -q  (p^q)  ~q-->(p^q)
_________________________________
  1   T  T   F    T       T 
  2   T  F   T    F       F
  3   F  T   F    F       T
  4   F  F   T    F       F

That's it. The truth table is TFTF which happens
to be the same as what's under q, so the expression
~q-->(p^q) is equivalent to q.  Later on, you'll show that
this way:

~q-->(p^q)       given
~(~q) v (p^q)    definition of conditional 
q v (p^q)        negation of a negation
(T^q) v (p^q)    tautology (T) is the indentity for conjunction    
 (Tvp)^q         factoring out ^q on the right 
    T^q          tautology (T) is the annihilator for disjunction
     q           tautology is the identity for conjunction
   
Edwin