Write the Word or Phrase That Best Completes Each Statement $P _ { n }$

Essay

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Let $P _ { n }$ be a statement involving the positive integer n, and let k be an arbitrary positive integer.
Proof by mathematical indicates that $P _ { n }$ is true for all positive integers n if
1. is true, and
2.The truth of $P _ { k }$ implies the truth of .