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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. $\forall x F\left[x\right]$
in Mathematical Logic by Boss (30.2k points)
recategorized by | 619 views

3 Answers

+3 votes
Best answer

~(∀x) F(x)

=(∃x)(~F(x))

So ans is C

by Veteran (62.7k points)
selected by
+1 vote

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

by (49 points)
0 votes

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

~(∀x) F(x)

=(∃x)(~F(x))

by Active (1.9k points)

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