Distributive law recognition in logic implementations Review the standard Boolean distributive identity: A · (B + C) = A · B + A · C. Decide whether this statement correctly represents the distributive law as implemented in logic.

Introduction / Context:
Distributive properties connect sums and products, guiding how logic networks can be factored or expanded. This identity is used both for algebraic simplification and for mapping to gate-level implementations.

Given Data / Assumptions:

• Boolean variables A, B, C in {0,1}.
• Operators: “+” for OR and “·” for AND.

Concept / Approach:
Distribution means a factor can be multiplied across each term inside parentheses. In Boolean algebra, A · (B + C) expands to A · B + A · C for all input combinations. This mirrors arithmetic distribution, albeit with Boolean operators.

Step-by-Step Solution:
If A=0: Left side 0 · (B + C) = 0; right side 0 · B + 0 · C = 0 + 0 = 0.If A=1: Left side 1 · (B + C) = B + C; right side 1 · B + 1 · C = B + C.Therefore, equality holds regardless of B and C.

Verification / Alternative check:
Truth-table enumeration confirms row-by-row equality. Karnaugh maps for both sides reduce to the same cover.

Why Other Options Are Wrong:
Conditional versions unnecessarily limit a universal identity; “Incorrect” contradicts a standard theorem used in all introductory texts.

Common Pitfalls:
Mixing up with the related identity A + (B · C) = (A + B) · (A + C). Forgetting operator meanings when switching between arithmetic intuition and Boolean logic.

Final Answer:
Correct