# Boolean Expression Simplification

## Homework Statement

Simplify the following expressions
(x'y'+xy'+x'y)

(p+q'p)(p+qr)

## Homework Equations

Laws of boolean algebra

## The Attempt at a Solution

For the first one I've found many ways to solve it... something isn't right here
(x'y'+xy'+x'y)
=x'(y'+y)+xy'
=x'+xy'
=x'+x+y'
=y'

OR

=y'(x'+x)+x'y
=y'+x'y
=y'+x'+y
=x'
I'm definantly doing something wrong here... probably making up laws For the second I'm not sure if the last line is even possible
(p+q'p)(p+qr)
=pp+pqr+ppq'+q'qr
=p+pqr+pq'+0
=p+pqr
=p? Can I do that with pqr having 3 variables?

ehild
Homework Helper
=x'+xy'
=x'+x+y'
=y'

That is wrong. Apply:

a+a'b=a+b

For the second question, replace the fist factor by p+q'p=p. You made a mistake in the derivation, but the result is p.

ehild

Ahh so the first is
=x'+y'

and with the second if I change it to:
p(p+qr)
won't I end up with
=p+pqr in the end anyway?

Also how do you know what rule you're supose to use? Is there a specific order or is it just whatever you notice first?

ehild
Homework Helper
and with the second if I change it to:
p(p+qr)
won't I end up with
=p+pqr in the end anyway?

I said the result was correct. You made a mistake as the last term was q'qpr, but it cancelled because of q'q.

Also how do you know what rule you're suppose to use? Is there a specific order or is it just whatever you notice first?

There are no general recipes.
Use what you notice first, but it helps if you notice when something cancels, for example E+a=E, a+a'=E, aa'=0. Factor out what you can, so a+ab=a(E+b)=a. But it is not a rule; sometimes you need to apply other tricks.

ehild

I said the result was correct. You made a mistake as the last term was q'qpr, but it cancelled because of q'q.

There are no general recipes.
Use what you notice first, but it helps if you notice when something cancels, for example E+a=E, a+a'=E, aa'=0. Factor out what you can, so a+ab=a(E+b)=a. But it is not a rule; sometimes you need to apply other tricks.

ehild

Ahh fair enough, thanks for the help.