Question

If A ⊂ B, show that (B’ – A’) = ϕ.

Answer 1

As A ⊂ B the set A is inside set B

Hence A ∪ B = B 

Taking compliment

⇒ (A ∪ B)’ = B’ 

Using De-Morgan’s law (A ∪ B)’ = A’ ∩ B’ 

⇒ A’ ∩ B’ = B’ …(i) 

Now we know that 

B’ = (B’ – A’) + (A’ ∩ B’)

Using (i) 

⇒ B’ = (B’ – A’) + B’ 

⇒ (B’ – A’) = B’ – B’ 

⇒ (B’ – A’) = 0 

⇒ (B’ – A’) = {ϕ} 

Hence proved