GATE CS 2026 Set 2 Q6 — Boolean Algebra

To determine which option is not a property of Boolean Algebra, let us evaluate each statement using the fundamental laws of Boolean Algebra:

• Option A ($a + b = b + a$): This is the Commutative Law for the OR ($+$) operation. It is a valid property.
• Option B ($a \cdot a' = 1$): According to the Complement Law, the AND ($\cdot$) of any variable with its complement is always $0$ (i.e., $a \cdot a' = 0$). For example, if $a = 1$, then $a' = 0$, giving $1 \cdot 0 = 0$. Thus, this statement is incorrect and is not a property of Boolean Algebra.
• Option C ($a + a' = 1$): This is the Complement Law for the OR ($+$) operation. It is a valid property.
• Option D ($a \cdot b = b \cdot a$): This is the Commutative Law for the AND ($\cdot$) operation. It is a valid property.

Therefore, the statement in Option B is not a property of Boolean Algebra.