Associative law for logical OR — evaluate the statement: “A + (B + C) = (A + B) + C” for Boolean variables A, B, C.

Introduction / Context:
Boolean algebra mirrors several familiar algebraic laws but with logical operators. The associative law establishes that grouping (parentheses) does not change the outcome for repeated OR or repeated AND operations. This property is fundamental when simplifying logic expressions and designing gate networks.

Given Data / Assumptions:

• A, B, C are Boolean variables (0 or 1).
• Operator “+” denotes logical OR.
• No timing hazards or non-ideal hardware effects are considered—pure logic algebra.

Concept / Approach:
Associativity of OR states that A + (B + C) = (A + B) + C = A + B + C. Because OR is associative, the order of evaluation (grouping) does not alter the truth table. This enables regrouping terms freely to match gate fan-in or to combine like terms during simplification without affecting functionality.

Step-by-Step Solution:

Verification / Alternative check:
Use set theory analogy: OR corresponds to union; union is associative: A ∪ (B ∪ C) = (A ∪ B) ∪ C. Alternatively, apply Boolean algebra axioms where associativity is a postulate.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing associativity with commutativity or distributivity; all three are valid but serve different rearrangements. Another pitfall is mixing OR with XOR; XOR is also associative but has different algebraic properties.

Final Answer:
Correct