The boolean expression \(\overline{A} \cdot B + A \cdot \overline{B}+ A \cdot…

2018

The boolean expression \(\overline{A} \cdot B + A \cdot \overline{B}+ A \cdot B\) is equivalenet to

  1. A.

    \(\overline{A} \cdot B\)

  2. B.

    \(\overline{A+B}\)

  3. C.

    \(A \cdot B\)

  4. D.

    \(A+B\)

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Correct answer: D

Simplify the expression: ¬A·B + A·¬B + A·B

  1. Group terms that contain A: A·¬B + A·B = A·(¬B + B) = A·1 = A

  2. Substitute this back into the expression to get: ¬A·B + A

  3. Use distributive/absorption law: A + ¬A·B = (A + ¬A)·(A + B) = 1·(A + B) = A + B

Therefore the original expression is equivalent to A + B.

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