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Daniel J Smith Custom TMUA Set A Paper 2 · Q4

Paper 2Logic & proofNumber & counting

Let SS be the statement about integers nn:

(∗)(*) For every integer nn there exists an integer mm such that m>nm>n and mm is even

Which of the following statements is logically equivalent to the negation of (∗)(*)?

AFor some integer nn there exists an integer mm such that m>nm>n and mm is odd.
BFor some integer nn, if an integer mm is greater than nn then mm is even.
CFor every integer nn, if nn is even then there is no integer m>nm>n that is even.
DIt is not the case that there exists an integer mm which is greater than every integer nn and is even.
EFor every integer mm there exists an integer n<mn<m such that mm is odd.
FThere exists an integer nn such that there is exactly one even integer greater than nn.
GThere exists an integer nn such that for all integers mm, if m>nm>n then mm is not even.

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