For any two sets A and B, show that the following statements are equivalent: (i) A ∪ B = B (ii) A ∩ B = A
For any two sets A and B, show that the following statements are equivalent: (i) A ∪ B = B (ii) A ∩ B = A

Answers:

(i) A ∪ B = B

Proving, (iii)=(iv)

Let us take, A ∪ B = B

A ∩ B = A.

A ⊂ B and A ∩ B = A

Thus, (iii)=(iv) is proved.

(ii) A ∩ B = A

Proving, (iv)=(i)

Let us take, A ∩ B = A

A ⊂ B

A ∩ B = A and A⊂B

Thus, (iv)=(i) is proved.