Boolean algebra fundamentals — verify the commutative law statement Evaluate the claim: “The commutative law of Boolean addition states that A + B = A · B.” State whether this statement is correct or incorrect, and recall what the commutative law actually asserts.

Introduction / Context:
Foundational Boolean algebra laws are used every day to simplify logic expressions and design digital circuits. The commutative law is among the most basic. This question asks whether the commutative law of Boolean addition claims A + B = A · B, and invites you to recall the exact statement of the law.

Given Data / Assumptions:

• Binary variables A and B take values 0 or 1.
• “+” denotes Boolean OR, “·” denotes Boolean AND.
• We are checking the correctness of the stated identity.

Concept / Approach:
The commutative law in Boolean algebra states that the order of operands does not affect the result: A + B = B + A for OR, and A · B = B · A for AND. It does not equate OR with AND. Therefore, asserting A + B = A · B is generally false except in special trivial cases (e.g., when A = B = 0 or 1 simultaneously).

Step-by-Step Solution:
Recall: OR is commutative → A + B = B + A.Recall: AND is commutative → A · B = B · A.Compare with given claim: A + B = A · B. This equates different operators and is not a commutative statement.Test with A=1, B=0: A + B = 1; A · B = 0 → not equal.

Verification / Alternative check:
Truth-table sampling for any unequal inputs shows a mismatch between OR and AND. Only when A and B are both 0 or both 1 do the two expressions coincide, but commutative law must hold for all inputs.

Why Other Options Are Wrong:
Correct: Not true; it misstates the law. The choices suggesting conditional correctness still misrepresent the law, which speaks to operand order, not operator equivalence.

Common Pitfalls:
Confusing commutativity (operand order) with other identities or with DeMorgan’s theorems. Another pitfall is assuming OR and AND can be interchanged without context.

Final Answer:
Incorrect