Question

If X and Y are two sets such that n(X) = 17 ,

n(Y) = 23 and n (XUY ) = 38 , find n( X ∩ Y )​

Answer 1

Answer:

n(XUY) = n(X) + n(Y) - n(X∩Y)

Inserting the values,

38= 17+23 -n(X∩Y)

-n(X∩Y)= 38-40 = -2

n(X∩Y) = 2

Answer 2

Step-by-step explanation:

$\sf{\bold{\blue{\underline{\underline{Given}}}}}$

1. If X and Y are two sets
2. n(X) = 17n
3. n(Y) = 23
4. n(XUY ) = 38 ⠀⠀⠀

$\sf{\bold{\red{\underline{\underline{To\:Find}}}}}$

⠀• find n( X ∩ Y )⠀?⠀⠀

$\sf{\bold{\purple{\underline{\underline{Solution}}}}}$

Here,

$\rightsquigarrow$ n(X) = 17 ,

$\rightsquigarrow$ n(Y) = 23

$\rightsquigarrow$ n(XUY ) = 38⠀⠀⠀

we know that,

$\boxed{\underline{\underline{\sf\color{fuchsia}{n(XUY )=n(X)+n(Y)- n( X ∩ Y )}}}}$

so,

According to the question,

$\bold{ 38=17+23-n(X∩Y) }$ 

$\bold{ 38+40-n(X∩Y)  }$ 

$\bold{n(X∩Y)=40-2  }$ 

$\mapsto\tt{n(X∩Y)=2 }$      

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

$\therefore$ so the value of n(X∩Y)=2