Let X be a set and let P(X) denote the Boolean ring whose elements are the subsets of X, with addition being symmetric difference and multiplication being intersection.
Is P({1}) an integral domain? Is P({1,2}) an integral domain?
How would I prove/disprove these
Rephrasing what zero divisor means in this context may help you: Since the zero is the empty set, and intersection is the product, finding a zero divisor is equivalent to finding two non-empty sets whose intersection is empty.