GATE | GATE-CS-2006 | Question 28
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)
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.