633 views

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

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

is

1. $\forall x (\sim F\left[x\right])$
2. $\sim (\exists x) F\left[x\right]$
3. $\exists x (\sim F\left[x\right])​$
4. $\forall x F\left[x\right]$

recategorized | 633 views

~(∀x) F(x)

=(∃x)(~F(x))

So ans is C

by Veteran (63k points)
selected
+1 vote

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

by (49 points)

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

~(∀x) F(x)

=(∃x)(~F(x))

by Active (1.9k points)