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Let S be a set. Consider the algebraic structure (p(S),U,n). Taking union to be the additive operation and intersection to be the multiplicative operation,

Let S be a set. Consider the algebraic structure (p(S),U,n). Taking union to be the additive operation and intersection to be the multiplicative operation, investigate whether or not this algebraic structure is a commutative ring. That is, either prove or provide a counterexample for each property of a commutative ring. Bonus: Does this structure have zero divisors?

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Closed Under Addition Yes this algebraic structure is closed under addition union This is because the union of two sets in S is another set in S Close... blur-text-image
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