## question about algebra of sets [closed]

Hello,

I have question about sets. I need to prove that: X ∩ (Y - Z) = (X ∩ Y) - (X ∩ Z).

now, I tried to prove that from both sides of the equation but had no luck.

for example, I tried to do something like this: X ∩ (Y - Z) = X ∩ (Y ∩ Z') but now i don't know how to continue.

from the other side of the equation I tried to do something like that: (X ∩ Y) - (X ∩ Z) = (X ∩ Y) ∩ (X ∩ Z)' = (X ∩ Y) ∩ (X' ∪ Z') and from here I don't know what to do again.

I'm starting to think that maybe there is some misprint in this expression or something like this. I will be glad to hear how should I continue from here and what I did wrong. Thanks in advance.

-
distributive law – Andreas Blass Mar 28 2012 at 20:05
This is a good question but not for this site try math.stackexchange.com instead (cf FAQs for details). General hint: if you are unsure whether something like this is true, forget all formalism for a moment and spell out in words what the thing means and/or draw some diagrams. Second hint: there is no misprint and you are almost done. (So perhaps no need to reask.) – quid Mar 28 2012 at 20:11