Question

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

• A. $a + b = b + a$
• B. $a \cdot (b + c) = (a \cdot b) + (a \cdot c)$
• C. $a + a = 2a$
• D. $a + (b \cdot c) = (a + b) \cdot (a + c)$

Hint:

Remember the Idempotent Laws: $x + x = x$ and $x \cdot x = x$. There are no coefficients or exponents in Boolean Algebra.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Boolean Algebra deals with binary variables and logic gates. Unlike standard algebra, it follows specific laws like Idempotent, Commutative, and Distributive laws, where variables can only take values of 0 or 1.
Step 2: Detailed Explanation:
Let's examine each option:
- Option A: This is the Commutative Law for addition (OR). It is a valid property.
- Option B: This is the Distributive Law where AND distributes over OR. It is a valid property.
- Option D: This is the second Distributive Law unique to Boolean Algebra where OR distributes over AND. It is a valid property.
- Option C: According to the Idempotent Law, $a + a = a$. In Boolean logic, there is no concept of a coefficient "2" because the result of any logical OR of a variable with itself is simply the variable itself.
Step 3: Final Answer:
The expression $a + a = 2a$ is mathematically incorrect in the context of Boolean Algebra.