First, we can tell by inspection that
(p V q) is equivalent to
p for all values of
p and
q except when
p is false and
q is true. So, because
(p ^ p) is equivalent to
p, we can immediately eliminate all but one combination and that's when
p is false and
q is true. So, we can simply inspect that one case and see if they are logically equivalent. Of course, this problem is so easy that in the time it took me to explain this logic in English, I could have shown you all four states in a truth table. So, why don't I do that anyways...
Code:
true <=> true ^ (true V true ) <=> true
true <=> true ^ (true V false) <=> true
false <=> false ^ (false V true ) <=> false
false <=> false ^ (false V false) <=> false
As you can see, the two statements are logically equivalent.
QED.