1. Mark each statement True or False. Justify each answer (a) If S is a nonempty subset of , then there exists an element m ∈ S such that m ≥ k for all k ∈ S. (b) The principle of mathematical...

1. Mark each statement True or False. Justify each answer

(a) If S is a nonempty subset of
, then there exists an element m ∈ S such that m ≥ k for all k ∈ S.

(b) The principle of mathematical induction enables us to prove that a statement is true for all natural numbers without directly verifying it for each number.

2. Mark each statement True or False. Justify each answer.

(a) A proof using mathematical induction consists of two parts: establishing the basis for induction and verifying the induction hypothesis.

(b) Suppose m is a natural number greater than 1. To prove P (k) is true for all k ≥ m, we must first show that P (k) is false for all k such that  ≤ k