GATE CS 2024 Set 2 — Question 30

MSQ+1 / -0EasyBoolean Laws & TheoremsBoolean Algebra & Logic GatesDigital Logic

Digital Logic → Boolean Algebra & Logic Gates → Boolean Laws & Theorems

Last updated 20 August 2026

Question

For a Boolean variable

x

, which of the following statements is/are FALSE?

x \cdot 1 = x

x + 1 = x

x \cdot x = 0

x + \bar{x} = 1

(B) x + 1 = x; (C) x · x = 0

Evaluating each Boolean identity:
(A)

x \cdot 1 = x

: This is the Identity Law, which is TRUE.
(B)

x + 1 = x

: In Boolean algebra,

x + 1 = 1

. This statement is FALSE.
(C)

x \cdot x = 0

: In Boolean algebra,

x \cdot x = x

(Idempotent Law). This statement is FALSE.
(D)

x + \bar{x} = 1

: This is the Complement Law, which is TRUE.
Thus, statements (B) and (C) are FALSE.