Which one of the following predicate formulae is NOT logically valid ? Note…

GATE · 2020 · CS · Computer Science & IT

Which one of the following predicate formulae is NOT logically valid ?

Note that WW is a predicate formula without any free occurrence of xx.

  1. A.

    ∀x(p(x)∨W)≡∀x (px)∨W\forall x (p(x) \vee W) \equiv \forall x \: ( px) \vee W

  2. B.

    ∃x(p(x)∧W)≡∃x p(x)∧W\exists x(p(x) \wedge W) \equiv \exists x \: p(x) \wedge W

  3. C.

    ∀x(p(x)→W)≡∀x p(x)→W\forall x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W

  4. D.

    ∃x(p(x)→W)≡∀x p(x)→W\exists x(p(x) \rightarrow W) \equiv \forall x \: p(x) \rightarrow W

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