What am I missing about this Boolean expression expansion?

Question

Sorry if this is too basic, but I am working through Boolean Algebra and Its Applications and do not understand this expansion in the author's example 5 in section 1-6:

$$(A+X+Y)(A+B'+Y') \rightarrow (A+AX+B'X+XY'+AY+B'Y)$$

But where are $AB'$ and $AY'$?

$BY$ does not come due to expansion... – hola Oct 19 '14 at 05:43 — hola, Oct 19 '14 at 05:43

score 1 · Answer 1 · answered Oct 19 '14 at 05:36

1

I don't have that textbook, but notice that: \begin{align*} (A+X+Y)(A+B'+Y') &= A + (X+Y)(B'+Y') \\ &= A + (B'X + B'Y + XY' + YY') \\ &= A + B'X + B'Y + XY' \\ \end{align*}

answered Oct 19 '14 at 05:36

Adriano

41,576

daOnlyBG · Accepted Answer · 2014-10-20T00:16:19.883

1

I don't have this book, but I have some limited knowledge about boolean algebra. I believe this should help: $$A+AB'+AY'= A+AY',$$ by the absorption rule. Use it again to get: $$A+AY'=A.$$

edited Oct 20 '14 at 00:16

answered Oct 19 '14 at 09:01

daOnlyBG

2,711

Right! I'm not sure why he's not using the Law of Absorption on $AY$, but perhaps that becomes useful later in the simplification. – jds Oct 19 '14 at 23:17

What am I missing about this Boolean expression expansion?

2 Answers2