Question

A(B + C) = AB + AC; A + BC = (A + B)(A + C) represent which law ?

• A. Commutative
• B. Associative
• C. Distributive
• D. Idempotent

Hint:

Remember that "distributive" means you are "distributing" the outside operator over the terms inside the parentheses.

Answer 1

The Correct Option is C

Step 1: Analyze the given expressions. The question provides two fundamental identities of Boolean algebra:

\(A \cdot (B + C) = (A \cdot B) + (A \cdot C)\)
\(A + (B \cdot C) = (A + B) \cdot (A + C)\)

Step 2: Match these identities to the laws of Boolean algebra. These are the definitions of the Distributive Law. The first shows that AND (`.`) distributes over OR (`+`), and the second shows that OR (`+`) distributes over AND (`.`). This second property is unique to Boolean algebra and does not hold true for ordinary algebra.

Commutative law is \(A+B = B+A\).
Associative law is \(A+(B+C) = (A+B)+C\).
Idempotent law is \(A+A = A\).
The given expressions clearly represent the Distributive law.