Question

If A and B are sets and A ∪ B = A ∩ B then which of the following is(are) true?

1 Either one of A or B is empty set.

2 B is proper subset of A.

3 A = B.

4 A is proper subset of B.
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Answer 1

1) If A or B is empty set then ,

lets say A is empty set,

A U B = B & A Π B = Null set

2) If B is proper subset of A

A U B = A & A Π B = B

4) If A is proper subset of B

A U B = B & A Π B = A

So , the correct answer is 3) A = B

as , A U B = A U A = A

and A Π B = A Π A = A