4. Given statement variables p and q, verify the following logical equivalences by constructing a truth table for each part:

(a) (10 points) p (c p) p t

(b) (10 points) (p q) (p q) ( p q)

5. Given any statement variables p, q, and r,

(a) (10 points) Is p (q r) logically equivalent to (p q) ( p r)?

(b) (5 points) Is t (c t) c (c t)? Prove your answer by constructing the truth table of each statement form.