Question

If X and Y are two sets such that n ( X ) = 17, n ( Y ) = 23 and n $( X \cup Y )$ = 38, find n $( X \cap Y )$.

Answer 1

Given, X and Y are two sets such that
number of elements in X, n(X) = 17
number of elements in Y, n(Y) = 23
and number of elements in $(X\cup Y)$, $n(X\cup Y)$ = 38.

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

38 = 17 + 23 - $n(X\cap Y)$

$n(X\cap Y)$ = 40 - 38 = 2

hence, $n(X\cap Y)$ = 2

Answer 2

Answer:

n(X∩Y) = 2

Step-by-step explanation:

It is given that , X , Y are two sets .

n(X) = 17 , n(Y) = 23 ,

n( X∪Y ) = 38 , n( x∩Y ) = ?

****************************************

We know that ,

n(X∩Y) + n(X∪Y) = n(X) + n(Y)

******************************************

n(X∩Y) = n(X) + n(Y) - n(X∪Y)

= 17 + 23 - 38

= 40 - 38

= 2

∴ n(X∩Y) = 2

.....