If A and B are two sets such that n(A –B) = 24, n(B – A) = 19 and n(A B) = 11, find:

(i) n(A)


(ii) n(B)


(iii) n(A B)


Given:


n(A - B) = 24, n(B - A) =19 and n(A B) = 11


To Find:


(i) n(A)


We know that,


n(A) = n(A - B) + n(A B)


= 24 + 11


= 35


Therefore, n(A) = 35 …(1)


(ii) n(B)


We know that,


n(B) = n(B - A) + n(A B)


= 19 + 11


= 30


Therefore,


n(B) = 30 …(2)


(iii) n(A B)


We know that,


n(A B) = n(A) + n(B) – n(A B) {From (1) & (2) n(A) =35


and n(B) =30}


= 35 + 30 - 11


= 54


Therefore,


n(A B) = 54


1