most recent 30 from http://mathoverflow.net 2013-05-20T15:58:36Z http://mathoverflow.net/feeds/question/92497 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/92497/question-about-algebra-of-sets UG7JY 2012-03-28T20:00:51Z 2012-03-28T20:00:51Z

<p>Hello,</p> <p>I have question about sets. I need to prove that: X ∩ (Y - Z) = (X ∩ Y) - (X ∩ Z).</p> <p>now, I tried to prove that from both sides of the equation but had no luck.</p> <p>for example, I tried to do something like this: X ∩ (Y - Z) = X ∩ (Y ∩ Z') but now i don't know how to continue.</p> <p>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.</p> <p>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.</p>