Proof with set laws?

use only the set laws, to prove the following result for all sets A,B, C:





(A - B) - C = A - ( B u C )





( the u on the right hand side is a union symbol)

Proof with set laws?
I'll use u to denote the union (as you have). I'll use ^ to denote the intersection of two sets, and I'll use a small c to denote the complement of a set (for example, Ac will mean the complement of A).





(A - B) - C = (A ^ Bc) - C (definition of set difference)





(A ^ Bc) - C = (A ^ Bc) ^ Cc (definition of set difference)





(A ^ Bc) ^ Cc = A ^ (Bc ^ Cc) (associativity of intersection)





A ^ (Bc ^ Cc) = A ^ (B u C)c (DeMorgan's Law)





A ^ (B u C)c = A - (B u C) (definition of set difference).





I hope this is of some help to you.

lady palm