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Euclid Sample Paper 2 · Q4

Paper 2Logic & proofNumber & counting

Consider the statement:

For every real number xx, there exists a positive integer nn such that

x<n≤x+2.x<n\leq x+2.

Which is its logical negation?

AFor every real xx, every positive integer nn satisfies n≤xn\leq x or n>x+2n>x+2.
BThere exists a real xx and a positive integer nn such that n≤xn\leq x or n>x+2n>x+2.
CThere exists a real xx such that every positive integer nn satisfies n≤xn\leq x or n>x+2n>x+2.
DFor every real xx, there exists a positive integer nn such that n≤xn\leq x or n>x+2n>x+2.
EThere exists a positive integer nn such that every real xx satisfies n≤xn\leq x or n>x+2n>x+2.

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