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Reduce the Boolean expression (algebraic minimization): Simplify A + A'*B to the minimal SOP form.

Difficulty: Easy

Correct Answer: A + B

Explanation:


Introduction / Context:
This is a standard reduction exercise using distributive and complement laws to simplify an expression to minimal SOP. Recognizing common identities speeds the process.


Given Data / Assumptions:

  • Expression: A + A'*B.
  • Operators: + is OR, * is AND, ' is complement.


Concept / Approach:
Use the identity X + X'*Y = X + Y (a consequence of X + X' = 1 and distribution). Alternatively, apply the consensus-style factoring: A + A'*B = (A + A') * (A + B) = 1 * (A + B) = A + B.


Step-by-Step Solution:

Step 1: Write A + A'*B = (A + A') * (A + B).Step 2: Since A + A' = 1, the product reduces to 1 * (A + B).Step 3: Final result is A + B.


Verification / Alternative check:
Truth-table verification confirms equivalence across all input combinations.


Why Other Options Are Wrong:

A * B: Too restrictive; fails when A=1, B=0.A' + B: Not equivalent; flips A.A*B + B': Nonsensical mixture; not equivalent.1: Would be true for all inputs.


Common Pitfalls:
Forgetting that (X + X') = 1 and misapplying distribution.


Final Answer:
A + B

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