GATE | GATE-CS-2000 | Question 30

Let a, b, c, d be propositions. Assume that the equivalences a ↔ (b V-b) and b ↔ c hold. Then the truth value of the formula (a ∧ b) → (a ∧ c) ∨ d) is always
(A) True
(B) False
(C) Same as the truth value of b
(D) Same as the truth value of d


Answer: (A)

Explanation:

Notations (identities):

(aVb)⬄(a AND b)
(a∨b)⬄(a OR b)
(-a)⬄(NOT a)
(a=>b)⬄(–aVb)

This solution is contributed by Sandeep pandey.

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