Proving the identity of boolean equations

Thread Starter

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.
 

Thread Starter

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)

Please let me know. Thanks!!
 

Georacer

Joined Nov 25, 2009
5,182
Great! That's it! Just write your path of thoughts in sequential lines, like my post in this thread for example. (You don't have to use LaTex of course). It looks more official that way and is easier for people to follow.
 
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