For a Boolean variable $x$ , which of the following statements is/are FALSE?

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Solution

Step-by-step verified solution

Official answer: B) x + 1 = x; C) x . x = 0

Boolean Algebra and Minimization

Evaluating Boolean identities:

(A) $x \cdot 1 = x$ (Identity law, TRUE)
(B) $x + 1 = 1 \neq x$ (Null law / Annihilation, FALSE)
(C) $x \cdot x = x \neq 0$ (Idempotent law, FALSE)
(D) $x + \bar{x} = 1$ (Complement law, TRUE)

Therefore, statements B and C are FALSE.

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This Boolean Algebra and Minimization previous year question is Q30 of the GATE CSE 2024 Set 2 paper. Find more GATE CSE PYQs on Boolean Algebra and Minimization in Digital Logic, or browse all GATE CSE PYQs.

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Boolean Algebra and Minimization in GATE CSE

Boolean Algebra and Minimization has 36 GATE CSE PYQs across 23 papers from 2011 to 2026. 5 of them are 1-mark MSQs like this one, and GATE CSE 2024 Set 2 has 2.

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Independent practice explanation verified by the GateAI team. GATE is conducted by the IITs; question text follows the official paper.