(1) (5 pts) Is p (q r) the negation of (p q) (p r) ? Justify your answer.

(2) (5 pts) Consider the wff (p q) r. (2a) Write down its contrapositive.

(2b) Start with the contrapositive in (2a) and rewrite using logical equivalences so that the final wff involves only variables, their negations, conjunctions, and disjunctions.

(3) (5 pts) Consider (p (q r)) (( q)(p )). First, fill the two blanks so that the logical equivalence is correct. Then, prove the logical equivalence using any method.

(4) (15 pts) Consider the following arguments. If an argument is valid, then present a proof sequence; otherwise, prove that the argument is invalid. You are forbidden to use truth tables to justify your answers (but, you may use them otherwise). (4a) ((p r) (q r)) ((p q) r) (4b) ((q r) (p (q r))) (p r) (4c) ((p (q r)) (s r) (s t)) (t p)