Thread: Can someone help me simplify this boolean expression?

1. Can someone help me simplify this boolean expression?

Can someone please show me how to simplify this expression? I have no clue of how it's done so any help would be appreciated. Thank you!

x'y'+xz'+yz+x'yz'+xy'z

2. Re: Can someone help me simplify this boolean expression?

Hey elorabees.

Hint: Try using De-morgans laws on a few of the terms.

3. Re: Can someone help me simplify this boolean expression?

Originally Posted by chiro
Hey elorabees.

Hint: Try using De-morgans laws on a few of the terms.
Thanks for replying but I'm still lost.. I'm sorry, Discrete isn't one of my strongest courses.

4. Re: Can someone help me simplify this boolean expression?

Demorgans theorems are as follows:

(a+b)' = a'b' and
(ab)' = a' + b'

Try using these to convert terms to common ones and simplify using the other laws (namely distributive).

5. Re: Can someone help me simplify this boolean expression?

Okay, but what can I do with xz'? I don't know what to do when we have a variable with a complement and a variable without a complement together?

I just reduced this part:
x'y'+xz'+yz=x'+y'+xz'+yz=(x'+x)(x'+z')+(y'+y)(y'+z )=(x'+z')+(y'+z)=x'z'+(y'+z) , Can we get y'z from that? and can you tell me if that is right?

6. Re: Can someone help me simplify this boolean expression?

Just as a hint for these problems, you can double check your work by creating a truth table consisting of 0 and 1 for all variables to check whether two statements are equivalent. I recommend you do this to check your own answers.

7. Re: Can someone help me simplify this boolean expression?

Originally Posted by chiro
Just as a hint for these problems, you can double check your work by creating a truth table consisting of 0 and 1 for all variables to check whether two statements are equivalent. I recommend you do this to check your own answers.
Oh, okay.. I will next time but I really appreciate all your help. I worked on it a bit more and I found the solution, it turns out to be 1. Really grateful for all the hints. I hope you have a great day ahead!