Q:

Product of Sum canonical transformation

This question is related to Logic Gates calculation.
Why is:
G = ( A + B + C * C' ) = ( A + B + C )*( A + B + C')
where + is OR, * is AND, ' is NOT.

A:

For simplicity denote $X = A + B$ and $Y = C'$ 
$X + C * Y = (X + C) * (X + Y)$      (distributive law)   
Replace X by (A+B) and Y by C', you will have what you need to prove.

