GATE 2009
March 14, 2025GATE 2009
March 14, 2025GATE 2009
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Question 26
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Consider the following well-formed formulae:
- I. ¬∀x(P(x))
II. ¬∃(P(x))
III. ¬∃(¬P(x))
IV. ∃x(¬(P(x))
Which of the above are equivalent?
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I and III
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I and IV
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II and III
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II and IV
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Question 26 Explanation:
I) ¬∀x(P(x)) = ∃x(¬P(x)) [Demorgan’s Law]
II ) ¬∃x(P(x))= ∀x(~P(x))
III) ¬∃x(¬P(x)) = ∀x(P(x))
II ) ¬∃x(P(x))= ∀x(~P(x))
III) ¬∃x(¬P(x)) = ∀x(P(x))
Correct Answer: B
Question 26 Explanation:
I) ¬∀x(P(x)) = ∃x(¬P(x)) [Demorgan’s Law]
II ) ¬∃x(P(x))= ∀x(~P(x))
III) ¬∃x(¬P(x)) = ∀x(P(x))
II ) ¬∃x(P(x))= ∀x(~P(x))
III) ¬∃x(¬P(x)) = ∀x(P(x))