You do not have permission to edit this page, for the following reason:
You can view and copy the source of this page.
Templates used on this page:
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 $∃x(¬P(x))$.
GATECSE