Boolean algebra basics Which property allows operands to be reordered without changing the result, as in A + B = B + A or A · B = B · A?

Introduction / Context:
Recognizing the fundamental Boolean algebra properties is essential for simplifying logic expressions and designing efficient digital circuits. Reordering terms legally can lead to simpler implementations and fewer gates.

Given Data / Assumptions:

• Operations considered: logical addition (+, OR) and logical multiplication (·, AND).
• Examples: A + B = B + A and A · B = B · A.

Concept / Approach:
The commutative property states that the order of operands does not affect the outcome of an operation. This holds for both OR and AND in Boolean algebra. By contrast, the associative property concerns how operands are grouped, and the distributive property governs how one operation distributes over another.

Step-by-Step Solution:
Identify the transformation: swapping operand order without regrouping (A with B).Match to property definitions: “commutative” permits operand order reversal.Confirm that both OR and AND operations are commutative in Boolean algebra.

Verification / Alternative check:
Create simple truth tables for A + B and B + A (or A · B and B · A). Each pair of tables is identical for every input combination, verifying commutativity.

Why Other Options Are Wrong:
Associative: relates to grouping, e.g., (A + B) + C = A + (B + C), not operand order.Distributive: e.g., A · (B + C) = A · B + A · C; different concept.“Boolean”: not a specific property; it is the field of study itself.

Common Pitfalls:
Mixing up commutative with associative properties or assuming commutativity for operations that are not commutative in other algebras.

Final Answer:
commutative