GATE CS 2026 Set 1 — Question 21
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Digital Logic → Boolean Algebra & Logic Gates → Boolean Laws & Theorems
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Question
Consider the following Boolean expression of a function :Which of the following expressions is/are equivalent to ?
Correct answer
(A) P ⊕ Q; (C) P ⊕ Q
Solution
Let and .
The function is .Calculate terms:
Substitute back:
This is the XNOR function, denoted as or .Check options:
(A) is XNOR. Correct.
(B) is XOR. Incorrect.
(C) . This is XNOR. Correct.
(D) . Incorrect.
The function is .Calculate terms:
Substitute back:
This is the XNOR function, denoted as or .Check options:
(A) is XNOR. Correct.
(B) is XOR. Incorrect.
(C) . This is XNOR. Correct.
(D) . Incorrect.
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