Login/Sign Up
Home » 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?
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?
CBSE | Class 11 | Exercise 1.6 | Maths | NCERT | Sets
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:

Provided

n\text{ }\left( X\text{ }\cup \text{ }Y \right)\text{ }=\text{ }18

n\text{ }\left( X \right)\text{ }=\text{ }8

n\text{ }\left( Y \right)\text{ }=\text{ }15

This can be written as

n\text{ }\left( X\text{ }\cup \text{ }Y \right)\text{ }=\text{ }n\text{ }\left( X \right)\text{ }+\text{ }n\text{ }\left( Y \right)\text{ }\text{- }n\text{ }(X\cap Y)

Now, substitute the values

18\text{ }=\text{ }8\text{ }+\text{ }15\text{ }\text{- }n\text{ }(X\cap Y)

Calculating further

n\text{ }(X\cap Y)\text{ }=\text{ }23{-}18\text{ }=\text{ }5

As a result, we get

n\text{ }(X\cap Y)\text{ }=\text{ }5

i

More Material