Exam-style question
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Simplify the Boolean expression F = AB + A(NOT B) + (NOT A)B. State the Boolean identities or laws used at each significant step.
Model answer
What a good answer should say
- F = AB + A(NOT B) + (NOT A)B = A(B + NOT B) + (NOT A)B = A(1) + (NOT A)B = A + (NOT A)B = A + B Therefore, F = A + B.
Explanation
Why this works
First, factor A from the first two terms: AB + A(NOT B) = A(B + NOT B). The complement law gives B + NOT B = 1, and the identity law gives A AND 1 = A.
The remaining expression A + (NOT A AND B) simplifies using the absorption-related identity A + (NOT A AND B) = A + B.
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