Commutative law for OR and AND — according to the commutative property, the order of variables does not affect the result of A + B or A · B. Is this universally valid for Boolean variables?

Introduction / Context:
Commutativity is a fundamental property in Boolean algebra that simplifies expression manipulation and gate realization. It states that swapping operands in OR or AND does not change the outcome, allowing flexible wiring and algebraic rearrangement without altering logic functionality.

Given Data / Assumptions:

• A and B are Boolean variables (0 or 1).
• Operators: + for OR, · for AND.
• We assume ideal Boolean behavior independent of timing.

Concept / Approach:
For all combinations of A and B, the truth tables of OR and AND are symmetric under operand interchange. That is, A + B equals B + A and A · B equals B · A in every input case. This symmetry enables hardware optimization since gate inputs are interchangeable, and it supports algebraic simplifications in logic design and Karnaugh mapping.

Step-by-Step Solution:

Verification / Alternative check:
Use set theory analogy: union and intersection of sets are commutative (A ∪ B = B ∪ A; A ∩ B = B ∩ A). This mirrors Boolean OR/AND.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing commutativity with associativity or distributivity; all are valid but represent different transformation freedoms.

Final Answer:
Universally valid (Correct)