Q7 of 145 Page 47

If A ⊂ B, prove that B’ ⊂ A’.

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


More from this chapter

All 145 →
5

If A and B are two sets such that n(A) = 23, n(b) = 37 and n(A – B) = 8 then find n(A ∪ B).

Hint n(A) = n(A – B) + n(A ∩ B) n(A ∩ B) = (23 – 8) = 15.


6

If A and B are two sets such than n(A) = 54, n(B) = 39 and n(B – A) = 13 then find n(A ∪ B).

Hint n(B) = n(B – A) + n(A ∩ B) ⇒ n(A ∩ B) = (39 – 13) = 26.


 8

If A ⊂ B, show that (B’ – A’) = ϕ.

 9

Let A = {x : x = 6n N) and B = {x : x = 9n, n ϵ N}, find A ∩ B.