If A and B are two sets such that

Solution:

Given:

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

To Find:

(i) n(A)

We know that,

$n(A)=n(A-B)+n(A \cap B)$

$=24+11$

$=35$

Therefore, $n(A)=35 \ldots(1)$

(ii) $n(B)$

We know that,

$n(B)=n(B-A)+n(A \cap B)$

$=19+11$

$=30$

Therefore,

$n(B)=30 \ldots(2)$

(iii) $n(A \cup B)$

We know that,

$n(A \cup B)=n(A)+n(B)-n(A \cap B)\{$ From $(1) \&(2) n(A)=35$

and $n(B)=30\}$

$=35+30-11$

$=54$

Therefore,

$n(A \cup B)=54$