Difference between revisions of "GATE2009 q26"

Revision as of 20:04, 14 July 2014

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

Solution by Happy Mittal

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 $∃x(¬P(x))$.