Question

Suppose that P(n) is a propositional function. Determine for which positive integers n the statement P(n) must be true if: P(1) and P(2) is true; for all positive integers n, if P(n) and P(n+1) is true then P(n+2) is true.

(a) P(1)

(b) P(2)

(c) P(4)

(d) P(n)

I had been asked this question by my college professor while I was bunking the class.

Asked question is from Strong Induction and Well-Ordering topic in section Induction and Recursion of Discrete Mathematics

Answer 1

Correct answer is (d) P(n)

The best I can explain: By induction, we can prove that P(n) is true.