GATE CS 2024 Set 2 | Question 30

MSQ · 1 mark

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

  1. Option A: \(x.1 = x\)
  2. Option B: \(x + 1 = x\) (correct)
  3. Option C: \(x.x = 0\) (correct)
  4. Option D: \(x + \overline{x} = 1\)

Answer

(B), (C)

Explanation

Check each statement for \(x = 0\) and \(x = 1\):

  • A: \(x.1 = x\) is the identity law for AND, so it is true.
  • B: \(x + 1 = 1\) for every \(x\), so \(x + 1 = x\) fails when \(x = 0\). False.
  • C: \(x.x = x\) (idempotent law), so \(x.x = 0\) fails when \(x = 1\). False.
  • D: \(x + \overline{x} = 1\) is the complement law, so it is true.

The false statements are B and C.

Answer: B, C