Boolean logic simplification of $a * b' * c' * d' + a * b + b * d' + b * c * d$

Question

The expression $a * b' * c' * d' + a * b + b * d' + b * c * d $ becomes $a * b + a * c' * d' + b * c + b * d'$, but how can I show that? I can find any laws to solve this. Thanks in advance.

Answer 1

In other words

a(b+b'c'd')
b(d'+cd)

becomes

a(b+c'd')
b(d'+c)

Can you see why know? If not, try simplifying x+x'y. https://stackoverflow.com/questions/12998589/boolean-algebra-prove-that might help.