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Viluxent Set 1 Paper 2 · Q1

Paper 2Logic & proofNumber & counting

Let nn be a positive integer, and consider the statements

P:n2−1 is divisible by 24.Q:gcd⁡(n,6)=1.P:n^2-1\text{ is divisible by }24.\qquad Q:\gcd(n,6)=1.

Which one of the following is true?

APP is sufficient but not necessary for QQ
BPP is necessary but not sufficient for QQ
CPP is necessary and sufficient for QQ
DPP is neither sufficient nor necessary for QQ

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