1.Set Theory
easy

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

A

$5$

B

$5$

C

$5$

D

$5$

Solution

It is given that:

$n(X \cup Y)=18, n(X)=8, n(Y)=15$

$n(X \cap Y)=?$

We know that:

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

$\therefore 18=8+15-n(X \cap Y)$

$\Rightarrow n(X \cap Y)=23-18=5$

$\therefore n(X \cap Y)=5$

Standard 11
Mathematics

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