# 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?

**Solution:**

It is given that X and Y are two sets such that

n (X) = 8, n (Y) = 15 and n (X υ Y) = 18

We know that n(X υ Y) is,

n (X υ Y) = n (X) + n (Y) - n (X ∩ Y)

n (X ∩ Y) = n (X) + n (Y) - n (X υ Y)

= 8 + 15 - 18

= 23 - 18

= 5

**Therefore, n ( X ∩ Y ) = 5**

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6 Question 2

## 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?

**Summary:**

It is given that X and Y are two sets such that X υ Y has 18 elements, X has 8 elements and Y has 15 elements. The number of elements that X ∩ Y has is 5.