Hello all, I'm a newbie at sets and logic, and I would like some help, if possible.

Suppose A, B and C are sets. Prove these statements are equivalent:

A (symmetric difference) C (intersects) B (symmetric difference) C = empty set

A (intersects) B (is a subset of) C (is a subset of) A (union) B

A (symmetric difference) C (is a subset of) A (symmetric difference) B

I would like some guidance on how to go about starting this problem. I started out by writing out the definition for symmetric difference (i.e. A (symmetric difference) C is equivalent to A (union) C \ A (intersects) C.)