GATE 2026 CS (CS2) – Question 16

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

Which one of the following options is not a property of Boolean algebra?

Note: $+$ is OR, $\cdot$ is AND, and $'$ is NOT.

$a + b = b + a$
$a \cdot a' = 1$
$a + a' = 1$
$a \cdot b = b \cdot a$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $a \cdot a' = 1$

Explanation

In Boolean algebra, $a + b = b + a$ and $a \cdot b = b \cdot a$ are commutative laws, and $a + a' = 1$ is a standard complement law. However, $a \cdot a' = 0$, not 1. Therefore, option (B) is not a valid property.