# Boolean algebra

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.

Hurkyl
Staff Emeritus
Gold Member
Well, what have you done so far?

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

Would a truth table work?

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.

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

Hurkyl said:
Have you done anything on this problem, or just sit and stared at it?
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.

Hurkyl
Staff Emeritus