GATE | GATE CS Mock 2018 | Set 2 | Question 11

Consider these statements :
S1 : ∀ can be distributed over conjunction.
S2 : ∃ cannot be distributed over disjunction.
S3 : ∀ can be distributed over disjunction.
S4 : ∃ can be distributed over conjunction.
Which of the following is/are false statement(s) about quantifiers ?

(A) S2 and S3
(B) S1 and S4
(C) S1 , S2 and S4
(D) S2, S3 and S4.

Answer: (D)
Explanation: BY the rule of distributing quantifiers, we know that
∀ can be distributed over conjunction and ∃ can be distributed over disjunction.
Therefore, S2, S3 and S4 are False.

Option (D) is correct.

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