If A and B are two sets such that n(A)=12, n(B)=19 and `(A cup B)=26` then find.
(a) `n(A cap B)`
(b) `n(A-B)`
(c) `n(B-A)`

Explanation

`n(A)=12,n(B)=19,n(A cup B)=26`
Then, `(i)n(A cupB)=n(A)+n(B)-n(A capB)`
`Rightarrow 26=12+19-n(A cap B)`
`Rightarrow n(A capB)=31-26`
`therefore n(A cap B)=5`
(ii) `n(A-B)=n(A cup B)-n(B) or =n(A)-n(A cap B)`
=26-19 or =12-5
=7 or =7
(iii) `n(B-A)=n(A cup B)-n(A)" "or " "=19-5`
`=14" "or " "=14`