2. (25 pts) Construct a truth table, showing whether or not the following two statements are logically equivalent:

a) p (q r)

b) (p q) (p r)

3. (25 pts) If t is a tautology and c is a contradiction, use truth tables to show that

p ^ t = p and p ^ c =c.

4. (25 pts) Explain how you would account for all possible combinations of four independent digital inputs (a, b, c, and d) in a circuit by illustrating it in a truth table. Explain how this concept can be used to account for all possible binary codes in a memory register.