# 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?

**Solution:**

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

n (X) = 40, n (X υ Y) = 60 and n (X ∩ Y) = 10

We know that n(X υ Y) is,

**n (X υ Y) = n (X) + n (Y) - n (X ∩ Y)**

From this,

n (Y) = n (X ∩ Y) + n (X υ Y) - n (X)

= 10 + 60 - 40

= 70 - 40

= 30

**Therefore, n (Y) = 30**

Thus, the set Y has 30 elements

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6 Question 5

## 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?

**Summary:**

It is given that X and Y are two sets such that X has 40 elements, X ∪ Y has 60 elements and X ∩ Y has 10 elements. We have found that Y has 30 elements.