1. The problem statement, all variables and given/known data Use principle of Mathematical Induction, Prove N (set of natural numbers) is inductive. Prove ∅ is inductive 2. Relevant equations Principle of Mathematical Induction 3. The attempt at a solution For N Let S be a subset of N 1) 1 is element of S. 2) Suppose S is inductive for some natural numbers. If x is an element of S, then x+1 is an element of S. 3) By PMI, N is inductive for every natural number n. Is that correct? For ∅ Let S be a subset of ∅? I don't know how to start. Would anyone give me a hint? Thanks!