Mathematics

Mathematics

Problem

The following four statements are parts of a proof that the sum of two odd integers is even: P. Substitute x=2k+1x = 2k + 1 and y=2ℓ+1y = 2\ell + 1, where kk and ℓ\ell are integers. Q. x+y=2(k+ℓ+1)x + y = 2(k + \ell + 1). R. 2(k+ℓ+1)2(k + \ell + 1) is divisible by 22 and hence is even. S. Therefore, the sum of two odd integers is even. Which order arranges these statements into a logically correct paragraph proof? a) Q → P → R → S b) P → R → Q → S c) P → Q → R → S d) P → Q → S → R

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