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Clavis TMUA Set A Paper 2 · Q12

Paper 2Logic & proofGeometryNumber & counting

Consider the following statement:

For every positive integer nn there is a positive integer mm such that m2+nm^2+n is a perfect square.

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

AFor every positive integer nn there is a positive integer mm such that m2+nm^2+n is not a perfect square.
BFor every positive integer nn and every positive integer mm, m2+nm^2+n is not a perfect square.
CThere is a positive integer nn such that there is a positive integer mm for which m2+nm^2+n is not a perfect square.
DThere is a positive integer nn such that for every positive integer mm, m2+nm^2+n is not a perfect square.
EThere is a positive integer nn such that for every positive integer mm, m2+nm^2+n is a perfect square.
FThere is a positive integer mm such that for every positive integer nn, m2+nm^2+n is not a perfect square.
GFor every positive integer mm there is a positive integer nn such that m2+nm^2+n is not a perfect square.
HThere are positive integers nn and mm such that m2+nm^2+n is not a perfect square.

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