Taking U to be the universe of discourse, let R be the set of subsets of U and define the operations +, \*, for R by

$A + B \equiv A \cup B - A \cap B$

$A \circ B \equiv A \cap B$

for subsets A, B of U. Define $0 \equiv \emptyset$ and $e \equiv U$. Then $(R,0,e,+,\circ)$ is a ring.

Compute the solutions X to the equations below using only $A, B, +, \circ$

i. $A + X = 0$

ii. $A + X = B$

iii. $X = (A-B)(A+B)$

I understand that X in number i. should be A, and I found in ii. that X can be written as $B - A \cup (B' \cap A)$, but I can't write it in terms of $A,B,+,\circ$ like the question asks.