Q5 of 145 Page 47

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.


Given: n(A) = 23, n(B) = 37, n(A – B) = 8


Using the hint


n(A) = n(A – B) + n(A ∩ B)


⇒ 23 = 8 + n(A ∩ B)


⇒ n(A ∩ B) = 23 – 8


⇒ n(A ∩ B) = 15


Visualizing the hint given,



We know that n(A ∪ B) = n(A) + n(B) – n(A ∩ B)


⇒ n(A ∪ B) = 23 + 37 – 15


⇒ n(A ∪ B) = 45


Hence n(A ∪ B) = 45


More from this chapter

All 145 →
3

If n(A) = 3 and n(B) = 5, find:

(i) The maximum number of elements in A ∪ B,


(ii) The minimum number of elements in A ∪ B.


 4

If A and B are two sets such than n(A) = 8, n(B) = 11 and n(A ∪ B) = 14 then find n(A ∩ B).

 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.


 7

If A ⊂ B, prove that B’ ⊂ A’.