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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

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    $\begingroup$ Either you use your intuition to find the appropriate idea and then show that it is in fact the case, or you do all the calculations (since the case is rather small). $\endgroup$
    – user228113
    Commented May 13, 2018 at 17:14

1 Answer 1

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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.

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