GATE | GATE-CS-2006 | Question 28
A logical binary relation â–¡ ,is defined as follows:
Let ~ be the unary negation (NOT) operator, with higher precedence than â–¡.
Which one of the following is equivalent to A∧B ?
(A) (~A â–¡ B)
(B) ~(A â–¡ ~B)
(C) ~(~A â–¡ ~B)
(D) ~(~A â–¡ B)
(A)
C
(B)
D
(C)
B
(D)
A
Answer: (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.
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Last Updated :
28 Jun, 2021
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