Question

If X and Y are two sets such that n (X) = 17, n (Y) = 23 and n (X ∪ Y) = 38, find n (X ∩ Y).

Answer 1

The given data is,

n( X )=17 n( Y )=23 n( X∪Y )=38

n( X∪Y )=n( X )+n( Y )−n( X∩Y ) ∴n( X∩Y )=n( X )+n( Y )−n( X∪Y )

n( X∩Y )=17+23−38 =2 ​

Therefore, the value of n( X∩Y )=2 .