The equivalence of ¬ ∃ x Q (x) is :

The equivalence of ¬ ∃ x Q (x) is :
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The equivalence of

¬ ∃ x Q (x) is :

A. ∃ x ¬ Q (x)

B. ∀ x ¬ Q (x)

C. ¬ ∃ x ¬ Q (x) 

D. ∀ x Q (x)

Please scroll down to see the correct answer and solution guide.

Right Answer is: B

SOLUTION

Solution:

Concept:

Two quantifies used in predicate logic is : universal quantifies which is used to denote sentences with words like “all” or “every” and another is existential quantifier which is used to denote sentence with words like “some” or “there is a”

 

True

False

∀ x  (universal)

All

Atleast one false

∃ x (existential)

Atleast one true

For all x, if P(x) is false, if we are taking predicate as P(x)

 

Explanation:

Given statement is: ¬ ∃ x Q (x) is :

This negation ¬ will change the quantifier and also it negates the element with the quantifier.

So, it becomes.

∀ x ¬ Q (x)

Because negation of existential is universal quantifier or vice versa.

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