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Using Boolean Algebra, prove the following
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$1) AB+\bar AC+BC$ $=AB+\bar AC+BC(A+\bar A)$ $(A+\bar A=1$, Complementary law)

$=AB+\bar AC+ABC+\bar ABC$

$=AB+ABC+\bar AC+ABC$ (Associative law)

$=AB+\bar AC$ (Absorption law)

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