Prove that if a statement can be proved by strong mathematical induction, then it can be

Chapter 5, Problem 27

(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 property
P( 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, prove
1. Q(b) is true.
2. For any integer k ? b, if Q(k) is true then Q(k + 1) is true.