GATE Computer Science (CS) 2020 Solved Papers

Question : 63 of 65

Marks: +1, -0

Which one of the following predicate formulae is NOT logically valid? Note that W is a predicate formula without any free occurrence of x.

Solution:

∀ ×(P(x) → ω) ≡ ∀ x p(x) → ω

is worng
since

∀ ×[(p x) → ω]=∀ x[∼ P(x) ∨ ω]

=∀ {x}[∼ {P}( {x}) {V} ω]

=∼[∃ × {P}( {x})] {V} ω

≡ ∃ × {P}( {X}) → ω

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