Proving the Distributive Property of XOR in 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.

 

[Hurkyl]

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?

 

[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]

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

 

[Tony11235]

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]

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