CUET PG 2021 — Mathematics PYQ

Solution

For $P(k+1)$ to be evaluated or proved true in the inductive step, the statement for $n=k$ must be assumed true:

Breakdown of the Principle

The process follows these logical steps:

1. Base Case: Prove $P(1)$ is true.

2. Assumption (Inductive Hypothesis): Assume $P(k)$ is true for some integer $k$:

   $$P(k)=mk+5$$

3. Inductive Step: Use the assumption to show $P(k+1)$ is true:

   $$P(k+1)=m(k+1)+5$$

Conclusion:

Therefore, if $P(k+1)=m(k+1)+5$ is true by induction, then $P(k)=mk+5$ must have been assumed true.