boolean algebra question here very short?

Question

We have the Boolean expression Y=A'BC' + ABC'+A'BC

Simplify it. Now, this is what I did

Y=BC'(A'+A) +A'BC.

Now using idempotence

Y=BC' + A'BC=B(C'+A'C)

I just dont know how to continue this. The result in my book is Y=A'B+BC'

Answer 1

Given that Y=A'BC+ABC'+A'BC Now, we know that A+A=A, so, Y=A'BC'+A'BC'+ABC'+A'BC Y=A'BC'+A'BC+A'BC'+ABC' Y=A'B(C'+C)+BC'(A+A') we know that A+A'=1 so, Y=A'B+BC'