Question

If X and Y are two sets such that X ∪ Y has 18 elements, X has 8 elements and Y has 15 elements; how many elements does X ∩ Y have?

Answer 1

The given data is,

n( X )=8 n( Y )=15 n( X∪Y )=18

n( X∪Y )=n( X )+n( Y )−n( X∩Y ) ∴n( X∩Y )=n( X )+n( Y )−n( X∪Y ) (1)

n( X∩Y )=8+15−18 =5

Therefore, the value of n( X∩Y )=5 .