Which one of the following options is not a property of Boolean Algebra? Note: $+$ is OR operation, $.$ is AND operation, and $'$ is NOT operation

According to the fundamental postulates and properties of Boolean algebra:

1. Commutative Laws:

   • $a + b = b + a$ (Option A is a valid property)

   • $a \cdot b = b \cdot a$ (Option D is a valid property)

2. Complement Laws:

   • $a + a^{\prime} = 1$ (Option C is a valid property)

   • $a \cdot a^{\prime} = 0$

Option (B) states $a \cdot a^{\prime} = 1$, which is false since the logical AND of any variable with its complement is always $0$.

Hence, B is not a property of Boolean algebra.