SOLUTION: Construct a truth table for (~p⋁q) ↔ p

Start out putting TTFF under the p's and TFTF under the q

(~p ⋁ q) ↔ p
  T   T    T  
  T   F    T
  F   T    F
  F   F    F

Then under the ~ put the negation (opposite) of what's 
under the p.  That is FFTT and scratch what's under 
the p:

(~p ⋁ q) ↔ p
 FT   T    T  
 FT   F    T
 TF   T    F
 TF   F    F

Then under the ⋁ put F if there are F's on both sides of
it and T the other times, then scratch through the columns on 
the sides of it.  That is, TFTT.


(~p ⋁ q) ↔ p
 FT T T    T  
 FT F F    T
 TF T T    F
 TF T F    F

Then finally under the ↔ put the T if it has the same 
thing on the left of it that it has on the right of it, and F
otherwise.  That is, put TFFF, and scratch through what's
on both sides of it:

(~p ⋁ q) ↔ p
 FT T T  T T  
 FT F F  F T
 TF T T  F F
 TF F F  F F

The answer is TFFF which is also the
truth table for p⋀q, so the above
expression is equivalent to p⋀q.

Edwin