Question

if X,Y are two sets such that n(X)=17,n(Y)=23 and n(X unionY)= 38,find n(X intersection Y)​

Answer 1

$\huge{\boxed{\mathtt{\red{ANSWER}}}}$

n(X∪Y)=n(X)+n(Y)-n(X∩Y)

38=17+23−n(X∩Y)

n(X∩Y)=40-38=2 (Ans)

Answer 2

$\Large{\underline{\underline{\bf{Solution :}}}}$

☯ Given :

• n(XUY) = 38
• n(X) = 17
• n(Y) = 23

$\rule{200}{1}$

☯ To Find :

We have to find the people who like only tennis and people who like tennis.

$\rule{200}{1}$

☯ Explanation :

We know that,

$\large{\implies{\boxed{\boxed{\sf{n(XUY) = n(X) + n(Y) - n(X∩Y)}}}}}$

→ Putting Values in above formula

$\sf{\rightarrow 38 = 17 + 23 - n(X \cap Y)} \\ \\ \sf{\rightarrow 38 = 40 + n(X \cap Y)} \\ \\ \sf{\rightarrow n(X \cap Y) = 40 - 38} \\ \\ \sf{\rightarrow n(X \cap Y) = 2} \\ \\ \Large{\implies{\boxed{\boxed{\sf{n(X \cap Y) = 2}}}}} \\ \\ \sf{\therefore \: n(X \cap Y) \: = \: 2}$