Chapter 11.4, Problem 1PE

Let $P_n$ be a statement involving the positive integer $n$ and let $k$ be an arbitrary positive integer. Proof by mathematical $\text{\_\_\_\_\_\_\_}$ indicates that $P_n$ is true for all positive integers $n$ if (1) $\text{\_\_\_\_\_\_\_}$ is true, and (2) the truth of $P_k$ implies the truth of $\text{\_\_\_\_\_\_\_}$ .