I have a little problem with this expression:
x = (A'+B)(A+C)
I know it can be simplified to:
A'C+AB
since ive used some software to simplify it, but i simply can't see how it is done.
This is what i've done so far:
(A'+B)(A+C) =>
A'A + AB + A'C + BC =>
0 + AB + A'C + BC =>
AB + A'C + BC
I just fail to see how i can do this differently and get to the correct result.
So we are trying to prove:
AB + A'C + BC = AB + A'C
Using the Identity Law X = X1, the left side can become:
AB + A'C + BC1
Inverse Law 1 = X' + X
AB + A'C + BC(A + A')
Distributive Law X(Y + Z) = XY + XZ
AB + A'C + BCA + BCA'
Associative Law (XY)Z = X(YZ)
AB + A'C + ABC + A'BC
Commutative Law X + Y= Y + X
AB + ABC + A'C + A'BC
Distributive again
AB(1 + C) + A'C(1 + B)
Finally, the Null Law 1 + X = 1
AB(1) + A'C(1)
AB + A'C = AB + A'C