Difficulty: Easy
Correct Answer: Correct: Order does not change the result
Explanation:
Introduction: Commutativity is a bedrock law in Boolean algebra. It guarantees that operands can be swapped without altering the outcome for both OR and AND operations. This law simplifies algebraic manipulation and circuit realization.Given Data / Assumptions:
Concept / Approach: The commutative law states A + B = B + A and A * B = B * A. Because gate implementations also reflect these identities, physical circuits behave the same regardless of operand order at the input pins (assuming symmetric devices).Step-by-Step Solution:
Step 1: Write identities: A + B = B + A and A * B = B * A.Step 2: Confirm via truth tables that each pair of expressions yields identical outputs for all input pairs.Step 3: Conclude that order does not affect results for OR and AND.Verification / Alternative check:
Swap inputs on a two-input gate in a simulator; outputs remain unchanged across the entire input space.Why Other Options Are Wrong:
Incorrect: Contradicts standard Boolean law.Correct only for OR / only for AND: Both operators are commutative.Common Pitfalls:
Confusing commutativity with associativity or distributivity.Assuming physical pin labeling changes behavior; for symmetric gates it does not.Final Answer:
Correct: Order does not change the result
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