GATE | GATE-CS-2006 | Question 28

A logical binary relation □ ,is defined as follows: 

Let ~ be the unary negation (NOT) operator, with higher precedence than □. 

Which one of the following is equivalent to A∧B ? 

(A) (~A □ B)  
(B) ~(A □ ~B) 
(C) ~(~A □ ~B)   
(D) ~(~A □ B) 

(A)

D

(B)

C

(C)

B

(D)

A

Answer: (A)

Explanation:

In A∧B, we have 3 entries as False, and one as True. In table, it is opposite case, so we have to negate A □ B, moreover, we want True only when both A and B are true, so in 3rd entry (which becomes true after negation), we want both true, so we have to negate A also. 
So A ∧ B ≡ ~(~A □ B), so option (D) is correct.

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