The GATE Grind

GATE 2024 CS (CS2) – Question 30

Digital Logic · Boolean Algebra and Minimization · 1 mark · Multiple select

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

  1. $x.1=x$
  2. $x+1=x$
  3. $x.x=0$
  4. $x+\bar{x}=1$

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Show answer and explanation

Correct answer: (B) $x+1=x$; (C) $x.x=0$

Explanation

x+1 = 1 (not x) and x·x = x (not 0), so B and C are false. x·1 = x and x+x̄ = 1 are true.