If a ⊂ b, then a ∩ b = a ∪ b. always, sometimes, never

Hence, the property:

            A ∩ B = A ∪ B never hold .

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)