True or false a If S is a non empty subset of N then there exists an element m

True or false a if s is a non empty subset of n then

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3.1.1. True or false:(a) IfSis a non-empty subset ofN, then there exists an elementmSsuchthatmkfor allkS.(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 forallkm, we must first show thatP(k)is false for allksuch that1k < m. Solution: 7
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3.1.14. Prove that9n-4nis a multiple of5for allnN. 8
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  • Natural number, Prime number

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