Q4 of 145 Page 47

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).

Given: n(A) = 8, n(B) = 11, n(A ∪ B) = 14


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


⇒ 14 = 8 + 11 – n(A ∩ B)


⇒ 14 = 19 – n(A ∩ B)


⇒ n(A ∩ B) = 19 – 14


⇒ n(A ∩ B) = 5


Hence n(A ∩ B) = 5


More from this chapter

All 145 →
2

If A = ϕ then write P(A).

 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.


 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.