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Shalnov [3]
3 years ago
8

If A ⊂ B, then A ∩ B = A ∪ B. always sometimes or never

Mathematics
1 answer:
Lisa [10]3 years ago
6 0

Sometimes. Proof:

Assume A\subset B.

Let a\in A\cap B, so that a\in A and a\in B. Then of course a\in A\cup B, so A\cap B\subseteq A\cup B.

Now let a\in A\cup B, so that a\in A *or* a\in B. Since A\subset B, if a\in A then a\in B, so that a\in A\cap B. But if a\in B, then a\not\in A, so it's not always the case that a\in A\cap B, and therefore in general A\cup B\not\subseteq A\cap B.

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