Boolean algebra

1. Sep 13, 2005

Tony11235

With $$x \oplus y$$ defined to be (here I'm using x' as the complement of x) xy'+x'y, prove $$x(y \oplus z) = xy \oplus xz$$

I'm stuck. Any hint or help would be great.

2. Sep 14, 2005

Hurkyl

Staff Emeritus
Well, what have you done so far?

(I presume xy is the "and" operation, and x+y is the "or" operation?)

3. Sep 14, 2005

Tony11235

Would a truth table work?

4. Sep 14, 2005

David

You can just expand out both expressions and see they are the same. You will need to use de Morgan's laws to turn the complement of a product into a sum of complements, however. That is the only tricky part.

5. Sep 14, 2005

Hurkyl

Staff Emeritus
Have you done anything on this problem, or just sit and stared at it?

6. Sep 14, 2005

Tony11235

I expanded the right side, thought deeply about it, tried a few other moves, but came up short and had to turn it in unfinished. Oh well, one low homework score won't kill me.

7. Sep 14, 2005

Hurkyl

Staff Emeritus
Well, if you had showed what you had done, maybe we could have pointed out the key step you were missing. Oh well.