UGC NET CSE | December 2014 | Part 3 | Question: 55

Question

Equivalent logical expression for the Well Formed Formula $(WFF)$,

$\sim(\forall x) F\left[x\right]$

is

• A. $\forall x (\sim F\left[x\right])$
• B. $\sim (\exists x) F\left[x\right]$
• C. $\exists x (\sim F\left[x\right])​$ 
• D. $\forall x F\left[x\right]$

Answer 1

~(∀x) F(x)

=(∃x)(~F(x))

So ans is C

Answer 2

Negation of all of 'x' is equal to there exist 'x', so C is the answer

Answer 3

When negation is brought before the atom, ∀ is converted to ∃ and vice versa.

~(∀x) F(x)

=(∃x)(~F(x))