As A ⊂ B the set A is inside set B

Hence A ∪ B = B

Taking compliment

⇒ (A ∪ B)’ = B.’

Using de-morgans law (A ∪ B)’ = A’ ∩ B.’

⇒ A’ ∩ B’ = B.’

A’ ∩ B’ = B’ means that the set B’ is inside the set A.’

Representing in Venn diagram,

As seen from Venn diagram B’ ⊂ A.’

Hence proved