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Return to GATE2009 q26.
Consider the following well-formed formulae:
I. ¬∀x(P(x))
II. ¬∃x(P(x))
III. ¬∃x(¬P(x))
IV. ∃x(¬P(x))
Which of the above are equivalent?
(A) I and III
(B) I and IV
(C) II and III
(D) II and IV
A formula ∀x(P(x)) is equivalent to formula ¬∃x(¬P(x)) i.e. add ¬ inside and outside, and
convert ∀ to ∃.
So, ¬∀x(P(x)) is equivalent to ∃x(¬P(x)). So option (B) is correct.
GATECSE