Boolean algebra identities: which option correctly states the commutative law in Boolean algebra (choose the statement that explicitly shows operands can swap order without changing the result)?

Introduction / Context:Boolean algebra underpins digital logic design. Several fundamental identities are frequently tested: commutative, associative, distributive, and idempotent laws. This question focuses on identifying the commutative law, which states that operands may be exchanged without affecting the result.

Given Data / Assumptions:

• Symbol “+” denotes logical OR; symbol “*” (or adjacency) denotes logical AND.
• We compare several identities to determine which one explicitly demonstrates operand interchangeability.
• Standard Boolean algebra rules apply.

Concept / Approach:The commutative laws are: A + B = B + A and A * B = B * A. They specifically show that the order of operands does not matter for OR or AND. Other identities (associative, distributive, idempotent) express different properties and should not be confused with commutativity.

Step-by-Step Solution:

Verification / Alternative check:Test with values: let A=0, B=1. A + B = 1 and B + A = 1, therefore the equality holds and demonstrates operand order irrelevance.

Why Other Options Are Wrong:

Common Pitfalls:Confusing distributive with commutative due to similar symbol patterns, and overlooking that commutativity solely concerns swapping operands, not grouping or distribution.

Final Answer:A + B = B + A