Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# In a class of 60 students, 25 students play cricket, 20 students play tennis and 10 students play both the games, then the number of students who play neither are(a). 0(b). 35(c). 45(d). 25

Last updated date: 14th Apr 2024
Total views: 327.9k
Views today: 10.27k
Verified
327.9k+ views
Hint: Find the number of students who play both cricket and tennis by finding $n\left( A\cup B \right)$. From this the students who play neither cricket nor tennis can be formed by subtracting from total students.

Given the total number of students in a class = 60.
Let ‘A’ be the set of students who play cricket, which is 25 in number.
$\therefore n\left( A \right)=25$
Let ‘B’ be the set of students who play tennis, 20 in number.
$\therefore n\left( B \right)=20$
The number of students who play both cricket and tennis is 10.
$\therefore n\left( A\cap B \right)=10$

The shaded area shows $A\cap B$.
The intersection of two sets A and B, consist of all elements that are both in A and B. The figure shows a Venn diagram representing the same.
Here, we are asked to find the number of students who don’t play cricket or tennis. Thus we need to find $\left( A\cup B \right)$ and subtract it from the total number of students.
$A\cup B$ is A union B, which means creating a new set containing every element from either of A and B.
The given Venn diagram represents $A\cup B$.

Hence, $n\left( A\cup B \right)=n\left( A \right)+n\left( B \right)-n\left( A\cap B \right)$
This formula can be directly derived from the above Venn diagram,
$\therefore n\left( A\cup B \right)=25+20-10=35$.
Here, 35 students play at least one out of cricket or tennis out of 60 students in a class.
$\therefore$The number of students who play neither cricket nor tennis =
Total students – number of students who play at least one game
= Total students - $n\left( A\cup B \right)$
= 60 – 35 = 25
$\therefore$The number of students who play neither cricket nor tennis = 25.
Hence, option (d) is the correct answer.

Note: A Venn diagram is used to represent all possible relations of different sets. Here we used $A\cap B$, which is the intersection of 2 sets to represent the common elements in both set A and B. And $A\cup B$represents the combined elements of set A and B.
Care should be taken not to confuse between $A\cap B$ and $A\cup B$.