Prove that if a statement can be proved by strong

Chapter 5, Problem 27E

(choose chapter or problem)

Prove that if a statement can be proved by strong mathematical induction, then it can be proved by ordinary mathematical induction. To do this, let P (n) be a property that is defined for integers n, and suppose the following two statements are true:1. P(a), P(a + 1), P(a + 2),..., P(b)________________.2. For any integer k ? b, if P (i) is true for all integers i from a through k, then P (k + 1) is true.The principle of strong mathematical induction would allow us to conclude immediately that P (n) is true for all integers n ? a. Can we reach the same conclusion using the principle of ordinary mathematical induction? Yes! To see this, let Q(n) be the propertyP (j) is true for all integers j with a ? j ? n.Then use ordinary mathematical induction to show that Q(n) is true for all integers n ?b. That is, prove1. Q(b) is true.________________2. For any integer k ?b, if Q(k) is true then Q(k + 1) is true.