Question

If X and Y are two sets such that $( X \cup Y )$ has 18 elements, X has 8 elements and Y has 15 elements many elements does $( X \cap Y )$ have?

Answer 1

Hey user

Here is your answer :-

Given :-

n$( X \cup Y )$ = 18

n ( X ) = 8

n ( Y ) = 15

To find :-

n$( X \cap Y )$ = ?

Solution :-

n$( X \cap Y )$ = n( X ) + n( Y ) - n$( X \cup Y )$

= 8 + 15 - 18

= 23 - 18

= 5.

so

$( X \cap Y )$ = 5.

Thank you.

Answer 2

Given, X and Y are two sets such that,

number of elements in set X , n(X) = 8

number of elements in set Y , n(Y) = 15

number of elements in set (X U Y), n(X U Y) =18

we have to find number of elements in X$\cap$Y

use formula,
n(X ∪ Y) = n(X)+ n(Y) - n(X ∩ Y)

⇒ 18 = 8+15 - n(X ∩ Y)

⇒ 18 = 23 - n(X ∩ Y)

⇒ n(X ∩ Y) = 23 - 18

∴ n(X ∩ Y) = 5