Express the negation of the statement, Mathematics

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States the negation of the statement ∀x ∃y (xy = 1) so that no negation precedes a quantifier.

Ans: The negation of the following statement is written as ~ [∀x ∃y (xy = 1)]. And

~[∀x ∃y (xy = 1)] = ∃x [~∃y (xy = 1)]

= ∃x ∀y [~(xy = 1)]

= ∃x ∀y (xy ≠ 1)

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