Question

If A and B are two sets such that A ⊂ B then what is A ∪ B?

Answer 1

If A and B are two sets such that A ⊂ B then is A ∪ B is B because all elements of A are present in B .

Answer 2

Let x ∈ A∪B

⇒ x ∈ A or x ∈ B

Since , A⊂B

⇒ x ∈ B

But x is an arbitrary element of set A∪B.

A∪B⊂B .........(1)

Let y ∈ B

⇒ y ∈ A∪B

But y is an arbitrary element of set B.

B⊂A∪B  ........(2)

From (1) and (2) , we get

A∪B = B