<s>[INST] Simplify the boolean function below by using algebra laws. I've been stuck on this question for some time, if anyone happens to solve it please explain step by step. 
$$(A +B ) \times ( A' + C ) \times ( B + C )$$
 [/INST] $(A +B ) \times ( A' + C ) \times ( B + C ) = [(A+B)\times A' + (A+B)\times C]\times (B+C) $
=$[A\times A'+B \times A' + A \times C + B \times C]\times (B+C) $
$A \times A' =0$
So, $B \times B \times A' +B \times A' \times C + A \times B \times C +A \times C \times C + B \times B \times C + B \times C \times C$
=$A' \times B + A' \times B \times C+ A \times B \times C+A \times C +B \times C = A' \times B + A \times C + B \times C$
write $B \times C$ as $A \times B \times C + A' \times B \times C$
=$ A' \times B + A \times C + A \times B \times C + A' \times B \times C$
=$A' \times B  + A' \times B \times C+ A \times C + A \times B \times C$
=$A' \times B + A \times C$
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