If A, B, and C are sets, prove that:?

C \ (A and B) = (C \ A) or (C \ B).

If A, B, and C are sets, prove that:?
Just do a mutual inclusion argument.


Say x is in C \ (A and B). Then x isn't in both A and B, and so in particular must not be in one of them (or if you like, in the complement of one of them). Say x is not in A. Then x is in C\A, and so in (C \ A) or (C \ B). Similarly, if x is not in B, then it is in C\B and also (C \ A) or (C \ B).





Now the other way. Say x is in (C \ A) or (C \ B). If x is in C\A, then x must be in C, but cannot be in A. Therefore x is also not in (A and B), and so x is in C\(A and B). Same thing works if x is in C\B.
Reply:uhh you can try substituting numbers in for the letters like 3, 4, 5 and see if they come out equaling each other.
Reply:Those are letters of the alphabet.