Boolean algebra identities: Which option correctly states the commutative law of Boolean multiplication (AND operation)?

Introduction / Context:The commutative law is a cornerstone of Boolean algebra and digital logic design. For multiplication (AND), it states that the order of operands does not affect the result. Recognizing commutativity allows flexible gate-level wiring and algebraic manipulation without altering circuit behavior.

Given Data / Assumptions:

• Boolean operators: + denotes OR, juxtaposition or · denotes AND.
• We focus on the AND operation’s commutative property.

Concept / Approach:For any Boolean variables A and B, AB = BA. This matches the physical reality of an AND gate: swapping inputs does not change the output. A similar law holds for OR: A + B = B + A. Knowing both is essential for logic reduction and schematic symmetry.

Step-by-Step Solution:Identify expressions that only swap operand order for AND.AB = BA is the precise statement of commutativity for AND.Therefore, select AB = BA.

Verification / Alternative check:Create a two-variable truth table; compute AB and BA for all four input combinations. The columns are identical, proving commutativity.

Why Other Options Are Wrong:A + B = B + A: This is commutativity of OR, not AND.AB = B + A: Mixes AND and OR; not an identity.AB = A × B (arithmetic form): Reads like arithmetic notation and does not state commutativity.A + AB = A: This is absorption, a different Boolean law.

Common Pitfalls:Confusing OR and AND properties or selecting identities that are true but address different laws (e.g., absorption or idempotence).

Final Answer:AB = BA