Question: Let S be a set. Consider the algebraic structure ((S),,). Taking union to be the additive operation and intersection to be the multiplicative operation, investigate

Let S be a set. Consider the algebraic structure ((S),,). 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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