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Clavis TMUA Set B Paper 2 · Q12

Paper 2Logic & proofNumber & counting

Consider the following statement:

There is a positive integer nn such that for every positive integer mm, m+nm+n is composite.

Which one of the following is the negation of this statement?

AThere is a positive integer nn such that for every positive integer mm, m+nm+n is prime.
BFor every positive integer nn there is a positive integer mm such that m+nm+n is prime.
CFor every positive integer nn and every positive integer mm, m+nm+n is prime.
DFor every positive integer nn there is a positive integer mm such that m+nm+n is composite.
EThere is a positive integer nn and a positive integer mm such that m+nm+n is prime.
FFor every positive integer mm there is a positive integer nn such that m+nm+n is prime.
GThere is a positive integer mm such that for every positive integer nn, m+nm+n is prime.
HFor every positive integer nn and every positive integer mm, m+nm+n is composite.

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