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3.1.1. True or false:(a) IfSis a non-empty subset ofN, then there exists an elementm∈Ssuchthatm≥kfor allk∈S.(b) The principle of mathematical induction enables us to prove a statementis true for all natural numbers without directly verify it for each number.Solution:(b) True by the definition.3.1.2. True or false:(a) A proof using mathematical induction consists of two parts: establishingthe basis for induction and verifying the induction hypothesis.(b) Supposemis a natural number greater than 1. To proveP(k)is true forallk≥m, we must first show thatP(k)is false for allksuch that1≤k < m.Solution:7
3.1.14. Prove that9n-4nis a multiple of5for alln∈N.8