All of them are part of one question. Please answer all of the sub-questions (a-f). Show all the steps and the laws used beside it.

9. For each of the following pairs of propositions, show that the two propositions are logically equivalent by finding a chain of equivalences from one to the other. State which definition or law of logic justifies each equivalence in the chain. a) p(qp),pq b) (p)q,pq c) (pq)q,pq d) p(qr),(pq)r e) (pr)(qr),(pq)r f) p(pq),p