Fill in the blanks in the proof of the following theorem.
THEOREM: A ⊆ B iff A ∪ B = B.
Proof: Suppose that A ⊆ B. If x ∈ A ∪ B, then x ∈ A or x ∈ ____
Since A ⊆ B, in either case we have x ∈ B. Thus____ ⊆ ____. On the other hand, if x ∈ ___ _, then x ∈ A ∪ B, so ____⊆ ____. Hence A ∪ B = B.
Conversely, suppose that A ∪ B = B. If x ∈ A, then x ∈ ____. But A ∪ B = B, so x ∈ ____ . Thus ____ ⊆ ____.
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