If X and Y are two sets such that X cup Y has 18 elements, X has 8 elements and Y has 15 elements ;

English

Gujarati

Hindi

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

Share

Similar Questions

If $S$ and $T$ are two sets such that $S$ has $21$ elements, $T$ has $32$ elements, and $S$ $\cap \,T$ has $11$ elements, how many elements does $S\, \cup$ $T$ have?

easy

If $A = \{ x:x$ is a natural number $\} ,B = \{ x:x$ is an even natural number $\} $ $C = \{ x:x$ is an odd natural number $\} $ and $D = \{ x:x$ is a prime number $\} ,$ find $A \cap D$

easy

If $\mathrm{R}$ is the set of real numbers and $\mathrm{Q}$ is the set of rational numbers, then what is $\mathrm{R – Q} ?$

easy

$A-(A-B)$ is

easy

$A$ and $B$ are two subsets of set $S$ = $\{1,2,3,4\}$ such that $A\ \cup \ B$ = $S$ , then number of ordered pair of $(A, B)$ is

hard