Boolean simplification (sum-of-products): Simplify the expression AB + A'B to its simplest form using Boolean algebra laws.

Introduction / Context:
Simplifying Boolean expressions reduces gate count, power, and delay. The expression AB + A'B is a common pattern that can be minimized using standard identities. Recognizing these patterns is essential in manual algebra and when checking tool results.

Given Data / Assumptions:

• Expression: F = AB + A'B (where A' denotes NOT A).
• Variables A and B are independent Boolean variables.
• Goal: obtain the simplest logically equivalent form.

Concept / Approach:
Use the Distributive and Absorption laws. Note that both product terms share B. Factor B, then apply the Complementarity law A + A' = 1. This often collapses the expression to a single literal or a simpler term.

Step-by-Step Solution:

Verification / Alternative check:
Truth-table check: when B = 0, both AB and A'B are 0 → F = 0; when B = 1, either A or A' is 1 → AB + A'B = 1 → F = 1. This matches F = B for all A.

Why Other Options Are Wrong:

Common Pitfalls:
Forgetting to factor the common literal; misreading A'B as A + B; confusing A + A' (which equals 1) with A * A' (which equals 0).

Final Answer:
B