A-(BuC) = (A-B)n(A-C)?

a,b,c are sets. i know this is true but i'm needing some help coming up with the proof. any ideas or directions are greatly appreciated. thanks

A-(BuC) = (A-B)n(A-C)?
Whenever you're out to show the equivalence of two sets, you need to show that each is a subset of the other. So in our case, start with showing that A-(BuC) is a subset of (A-B)n(A-C), then vice versa.





To show that a set is a subset of another, we take any element from the first and show that it is also in the second.





So let x be in A-(BuC). Then (by def. of "-") x is in A and x is not in (BuC). Since x is not in BuC, x is not in B and x is not in C. Since x is in A but not B, x is in (A-B). Since x is in A but not in C, x is in (A-C). Since it's in both, it's in the intersection.





This argument shows that the first set is a subset of the second. This argument is nice because you can pretty much reverse its steps in building a proof that the second set is a subset of the first. After you've done this, you're done.

kudzu