Let p(n) be the statement that n! < nn, where n is an integer greater than 1. a) what is the statement p(2)? b) show that p(2) is true, completing the basis step of a proof by mathematical induction that p(n) is true for all integers n greater than 1. c) what is the inductive hypothesis of a proof by mathematical induction that p(n) is true for all integers n greater than 1? d) what do you need to prove in the inductive step of a proof by mathematical induction that p(n) is true for all integers n greater than 1? e) complete the inductive step of a proof by mathematical induction that p(n) is true for all integers n greater than 1. f ) explain why these steps show that this inequality is true whenever n is an integer greater than 1.