The symmetric difference operation on sets is , defined by X  Y = (XY)-(XY).
Let A be any set and let R=(A) be the set of all subsets of A ? the "power set" of A. We will consider symmetric difference to be the "addition" operation on R, the better known operation of intersection to be the "multiplication" on R. It is a fact that R with these two operations is a commutative ring with unity. The first few parts of this problem ask about some of details about this ring.

(a) What is the zero of R? That is, what set Z has the property that XZ=ZX=X?

(b) What is the unity of R?

(c) If X an element of R (i. e. some subset of A), what is the additive inverse of X?

(d) What elements of R has a multiplicative inverse in R?