S(n) is a statement about positive integers n suchthat whenever S( k ) is true,

Question

S(n) is a statement about positive integers n suchthat whenever S(k) is true, S(k + 1) must also betrue. Fuethermore, there exists some positive integern0 such that S(n0) isnot true. Of the following which is the strongest conclusionthat can be drawn. A.) S(n0 + 1) is not true. B.) S(n0 -1) is not true. C.) S(n) is not true for any n <n0. D.) S(n) is not true for any n > n0 E.) S(n) is not true for any n. Please include an explanation Thanks S(n) is a statement about positive integers n suchthat whenever S(k) is true, S(k + 1) must also betrue. Fuethermore, there exists some positive integern0 such that S(n0) isnot true. Of the following which is the strongest conclusionthat can be drawn. A.) S(n0 + 1) is not true. B.) S(n0 -1) is not true. C.) S(n) is not true for any n <n0. D.) S(n) is not true for any n > n0 E.) S(n) is not true for any n. Please include an explanation Thanks E.) S(n) is not true for any n. Please include an explanation Thanks

Explanation / Answer

this is essentially talking about mathematical induction where the first step is to find an n sub 0 such that your claim holds and then assume n to show n+1. It really doesnt matter if n sub 0 is greater than one because these are just exceptions. Your answer is C)

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