How to simplify the following expression using boolean algebra?

Question

How to simplify the following expression using boolean algebra?

a[b'c+ (b+c')'](a'b+c)

Answer 1

We have A[B'C + (B+C')'](A'B + C)=

for Moore's Law we have (B+C')'=B'C :
=A[B'C + B'C](A'B + C) = [AB'C + AB'C](A'B + C) =

Multiplying :
= [AB'C + AB'C](A'B + C) =

X+X=X then AB'C + AB'C = AB'C:
= AB'C (A'B + C) =

Multiplying :
=AB'CA'B + AB'CC=

we have that X*X'=0 so AB' * A'B * C = 0 * C= 0 and we have that X*X=X so AB'C*C= AB'C

The final result is : = AB'C