Reduce the boolean equation to simplest form. I have finished the problem, I just need help to verify if what I've done is correct.

Question

I did all the work already. I was wondering if simplified the solution, I got at the last line was right. Thanks for the help! (please ignore the => )

Answer 1

Couple of issues:

That first step is Distribution, not Absorption

Also, $B'C'+BC'+BC \overset{Adjacency}{=}B'C'+B\overset{Reduction}{=}C'+B$

Likewise, $B'C'+B'C+BC'=B'+BC'=B'+C'$

So, your expression can be simplified to:

$A'(C'+B)+A(B'+C')$

But that's still not the simplest, because you can continue with:

$A'C'+A'B+AB'+AC'=C'+A'B+AB'=C'+(A \oplus B)$