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
- A.
\(\overline{A} \cdot B\) - B.
\(\overline{A+B}\) - C.
\(A \cdot B\) - D.
\(A+B\)
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Correct answer: D
Simplify the expression: ¬A·B + A·¬B + A·B
Group terms that contain A: A·¬B + A·B = A·(¬B + B) = A·1 = A
Substitute this back into the expression to get: ¬A·B + A
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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