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 )

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1.Set Theory

easy

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

A

$2$

B

$2$

C

$2$

D

$2$

Solution

It is given that:

$n(X)=17, n(Y)=23, n(X \cup Y)=38$

We know that:

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

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

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

$\therefore n(X \cap Y)=2$

Standard 11

Mathematics

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