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

GATE · 2016 · CS · Set 2 · Computer Science & IT

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

  1. A.

    (∀xp(x)⇒∀xq(x))⇒(∃x¬p(x)∨∀xq(x))(∀x p(x) ⇒ ∀x q(x)) ⇒ (∃x¬p(x) ∨ ∀x q(x))

  2. B.

    (∃xp(x)∨∃xq(x))⇒∃x(p(x)∨q(x))(∃x p(x) ∨ ∃x q(x)) ⇒ ∃x (p(x) ∨ q(x))

  3. C.

    ∃x(p(x)∧q(x))⇒(∃xp(x)∧∃xq(x))∃x (p(x) ∧ q(x)) ⇒ (∃x p(x) ∧ ∃x q(x))

  4. D.

    ∀x(p(x)∨q(x))⇒(∀xp(x)∨∀xq(x))∀x (p(x) ∨ q(x)) ⇒ (∀x p(x) ∨ ∀x q(x))

Attempted by 182 students.

Sign up free to check your answer

Sign up free

Explore the full course: Gate Guidance By Sanchit Sir

Loading lesson…