On the one hand, the union gathers all the elements occurring in at least one of the sets. As such, all of them are its subsets. For example, the union of two sets with one entirely contained in the other is equal to the larger one.
On the other hand, the intersection gathers all the elements common to each and every one of the sets. As such, it's a subset of each of them. For instance, the intersection of two sets with one entirely contained in the other is equal to the smaller one.
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