Discrete Math Set Theory Question

[Chandasouk]

Let A, B, and C be sets. Show that

a) (A-B) - C \subseteq A - C
b) (B-A) \cup (C-A) = (B \cup C) - A

I am using variable x to represent an element.

Part A)

I rewrote (A-B) - C as (x\inA ^ x\notinB) - C

I think this could be rewritten as
(x\inA ^ x\notinB) ^ x\notin C

A-C can be rewritten as (x \in A ^ x \notin C)

The original statement can be rewritten as

x\inA\cap~B\cap~C \subseteq x\inA\cap~C

where ~ represents negation.

However, for the LHS to be a subset of the RHS, all elements of the LHS should be an element of RHS but since the LHS has ~B, I don't think that it is a subset?

I have no idea how to show part B so any help would be great.

 

[jedishrfu]

when you draw a venn diagram you'll see that set A-C contains the intersection A,B and C but that A-B-C does not. perhaps you use that in your proof. I don't think venn diagrams can be used in proofs but they do help visualize the situation.