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

2 Answers

1 vote

The answer is never.

User Onimusha
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2 votes

Answer:

Hence, the property:

A ∩ B = A ∪ B never hold .

Explanation:

We are given that set A⊂B .

This means that set A is properly contained in set B.

i.e. A≠B

This means that there are some elements in set B which are not in set A.

Now we have to show whether the following property A∩B=A∪B

always, sometimes or never hold.

As A is a proper set of B.

This means that: A∩B=A ( Since A is a smaller set)

Also, A∪B=B (Since B is a bigger set)

Hence, A∩B ≠ A∪B (Since A≠ B)

User ElvisLives
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