GATE CS 2026 Set 2 Q.16: Boolean Algebra and Logic Minimization

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

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

$a + b = b + a$

$a . a' = 1$

$a + a' = 1$

$a . b = b . a$

Official answer and solution

Official answer: B
From: Official GATE 2026 answer key

Solution

Check the fundamental laws of Boolean algebra (commutativity and complementation).

In Boolean algebra, the AND complement law states that $a \cdot a' = 0$ (contradiction), whereas $a + a' = 1$ (excluded middle). Therefore, $a \cdot a' = 1$ is false and is not a property of Boolean algebra.

Final answer

Option (B)

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2026 Computer Science and Information Technology - Session 2 (CS2)
Question: 16 of 65
Section: Computer Science and Information Technology

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