please show your proofs too, using the logic equivalence laws. thanks!

Which of the following are tautologies? If the statement is a tautology give a proof using the appropriate rules of logic at each step of the proof. I prefer you to not use a truth table, but you can use rules of logic that we developed in class e.g., we showed that p q is equivalent to its contrapositive. You may also use (p q) (p q). If something is not a tautalogy, then justify your answer by giving a counterexample, i.e., a truth assignment which results in a false value. (a) (p q) (b) (p (p q)) q (c) [(p q) (p r) (q r)] r. (d) [(p q) r) [p (q r)]