Chapter 9.5, Problem 40E

Solution

To identify : The correct option for the statement “ The first step in a proof by mathematical induction is to prove”

Option (A) the anchor

Option (B) the inductive hypothesis

Option (C) the inductive step

Option (D) the inductive principle

Option (E) the inductive foundation

Option (A) is correct option.

Given information :

The statement for mathematical induction.

Explanation :

Consider any statement $P_n$ ,

To prove that it is true by mathematical induction, the following steps are followed.

Anchor step: Prove that any statement $P_n$ is true for $n=1$ .

Inductive hypothesis: Assume $P_n$ is true for $n=k$ .

Inductive Step: Prove that $P_n$ is true for $n=k+1$ .

Thus, the first step is anchor step where it is proved that $P_1$ is true.

So, the option (A) is correct.