# Proving the identity of boolean equations

#### mcc123pa

Joined Sep 12, 2010
40
Hi everyone:

I was assigned the following problem for homework:
Y+X'Z+XY'=X+Y+Z

The directions read: prove the identity of each of the following Boolean equations using algebraic manipulation.

I have tried some various attempts, such as factoring out X and X' or Y and Y' but have not made any progress.

Could someone please post the solution? Thanks!

#### Georacer

Joined Nov 25, 2009
5,182
There's a boolean identity saying that A+BC=(A+B)(A+C). Try to use that one.
HINT: Try the first and third term to begin with.

#### mcc123pa

Joined Sep 12, 2010
40
Thanks so much for the hint! I think I figured it out!

Is this correct? :

y+x'z+xy'= x+y+z (original equation)

(y+x)(y+y') (used the identity a+bc= (a+b)(a+c) as suggested)
(y+x)(1) (used the identity y+y'=1)
y+x+x'z =x+y+z (put the result of line three back into the original equation)
(x+x')(z+x) which in turn equals (z+x)(I did the same step as lines 2&3)
x+y+z=x+y+z (put the result from the line above back into the original equation)