using boolean algebra simplify following (overline A + B)(A+C)

Question

$(\overline{A} + B)(A + C)$

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Sure, let's simplify the given Boolean expression step by step.

Given expression: (A' + B)(A + C)

Step 1: Apply the distributive law, which states that A(B + C) = AB + AC.

So, (A' + B)(A + C) = A'A + A'C + BA + BC

Step 2: Apply the law of complementation, which states that AA' = 0.

So, A'A + A'C + BA + BC = 0 + A'C + BA + BC

Step 3: Apply the law of identity, which states that A + 0 = A.

So, 0 + A'C + BA + BC = A'C + BA + BC

So, the simplified Boolean expression is A'C + BA + BC.

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