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tmua.fyi Mock Paper 2 (2) · Q3

Paper 2Logic & proof

The statement ‘∀x∈R, ∃y∈R\forall x\in\mathbb R,\ \exists y\in\mathbb R such that xy=1xy=1’ is false. Which of the following is its negation?

A∀x∈R, ∃y∈R such that xy≠1\forall x\in\mathbb R,\ \exists y\in\mathbb R\text{ such that }xy\ne1
B∃x∈R such that ∀y∈R, xy≠1\exists x\in\mathbb R\text{ such that }\forall y\in\mathbb R,\ xy\ne1
C∃x,y∈R such that xy≠1\exists x,y\in\mathbb R\text{ such that }xy\ne1
D∀x,y∈R, xy≠1\forall x,y\in\mathbb R,\ xy\ne1
E∃x∈R such that ∃y∈R, xy=1\exists x\in\mathbb R\text{ such that }\exists y\in\mathbb R,\ xy=1

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