Boolean Algebra Properties Identification

The question asks to identify which of the given options is not a property of Boolean Algebra. We need to evaluate each option based on the standard laws of Boolean Algebra.

Analyzing Boolean Algebra Properties

• Option 1: $a + b = b + a$

  This is the Commutative Law for the OR operation. It holds true in Boolean Algebra.

• Option 2: $a . a' = 1$

  This statement represents a variable ANDed with its complement resulting in 1. The actual property of Boolean Algebra is the Complement Law, which states $a . a' = 0$. Therefore, this option is not a property of Boolean Algebra.

• Option 3: $a + a' = 1$

  This is the Complement Law for the OR operation. It states that a variable ORed with its complement always results in 1. This holds true in Boolean Algebra.

• Option 4: $a . b = b . a$

  This is the Commutative Law for the AND operation. It holds true in Boolean Algebra.

• Option 5: (Empty Option)

  This option is undefined and cannot be considered a property.

Conclusion: Non-Property Identified

The option $a . a' = 1$ contradicts the fundamental Complement Law ($a . a' = 0$) of Boolean Algebra. Hence, it is the correct answer as it is not a property.