Question

If X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements, how many elements does Y have?

Answer 1

The given data is,

n( X )=40 n( X∪Y )=60 n( X∩Y )=10

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

n( Y )=60+10−40 =70−40 =30​

Therefore, the number of elements in set n( Y ) is 30 .