GATE Computer Science (CS) 2016 Shift 2 Solved Paper

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Question : 37 of 65

Marks: +1, -0

Which one of the following well-formed formulae in predicate calculus is NOT valid?

(∀x p(x) ⇒ ∀x q(x)) ⇒ (∃x ¬ p(x) ∨ ∀x q(x))
(∃x p(x) ∨ ∃x q(x)) ⇒ ∃x (p(x) ∨ q(x))
∃x (p(x) ∧ q(x)) ⇒ (∃x p(x) ∧ ∃x q(x))
∀x (p(x) ∨ q(x)) ⇒ (∀x p(x) ∨ ∀x q(x))

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