If A ⊆ B and B ⊆ A, what can be concluded about A and B?

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Multiple Choice

If A ⊆ B and B ⊆ A, what can be concluded about A and B?

Explanation:
When A is a subset of B and B is a subset of A, every element of A is in B and every element of B is in A. That means A and B contain exactly the same elements, so they are equal. It can’t be a strict subset, because strict inclusion would mean one set has more elements than the other, which isn’t possible here. It also isn’t disjoint, since the two sets share all their elements. So the conclusion is that A and B are equal.

When A is a subset of B and B is a subset of A, every element of A is in B and every element of B is in A. That means A and B contain exactly the same elements, so they are equal. It can’t be a strict subset, because strict inclusion would mean one set has more elements than the other, which isn’t possible here. It also isn’t disjoint, since the two sets share all their elements. So the conclusion is that A and B are equal.

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