Boolean algebra

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.

Answers and Replies

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

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

Tony11235
Would a truth table work?

Science Advisor
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.

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

Tony11235
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.

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