Suppose A, B, and C are sets. Prove the following statements are equivalent.

(A∆C)∩(B∆C)=∅

(A∩B)⊆C⊆(A∪B)

(A∆C)⊆(A∆B)

Re-formatted because my first post was a little confusing to read.

The only thing I've done is re-write the symmetric differences out (i.e. (A∆C) is equivalent to (A∪C)\(A∩C)). A hint in the right direction would be much appreciated.