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

Solution:

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

n (X) = 17, n (Y) = 23 and n (X υ Y) = 38

We know that n(X υ Y) is,

n (X υ Y) = n (X) + n (Y) - n (X ∩ Y)

From this,

n (X ∩ Y) = n (X) + n (Y) - n (X υ Y)

= 17 + 23 - 38

= 40 - 38

= 2

Therefore, n ( X ∩ Y ) = 2

NCERT Solutions Class 11 Maths Chapter 1 Exercise 1.6 Question 1

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

Summary:

It is given that X and Y are two sets such that n (X) = 17, n (Y) = 23 and n (X υ Y) = 38. We have found that n ( X ∩ Y ) = 2.