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Let's say I am given a set that has a bunch of sets as its element, for instance, the power set of natural numbers less than or equal to 1, denoted as $P(1)$. Is it true that such kinds of sets, where the elements are sets, never form a group under a set operation? I am wondering what it means for sets to have inverses?

Four Seasons
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    "I am wondering what it means for sets to have inverses?" - This depends on the group law, i.e., how you compose sets. – Dietrich Burde Mar 31 '19 at 18:29
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    The symmetric difference makes it an Abelian group, moreover a vector space over the 2 element field. – Berci Mar 31 '19 at 18:50

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