Answer:
10
Step-by-step explanation:
Given that:
Total number of students = 50
Students who like to play football = 25
[tex]n(A) = 25[/tex]
Students who like to play cricket = 35
[tex]n(B) = 35[/tex]
Each student likes to play at least one game.
It means the universal set is equal to the union of the above two sets.
[tex]n(U) =n(A\cup B) = 50[/tex]
To find:
The number of students who play both the games and representation of the given situation in the form of a Venn diagram.
i.e. [tex]n(A\cap B) = ?[/tex]
Solution:
First of all, let us have a look at the formula for the number of elements in the union of two sets.
[tex]n(A\cup B)=n(A)+n(B)-n(A\cap B)[/tex]
Putting the values in the formula, we need to find the value of [tex]n(A\cap B)[/tex]
[tex]50=25+35-n(A\cap B)\\\Rightarrow 50-60=-n(A\cap B)\\\Rightarrow n(A\cap B)=\bold{10}[/tex]
Therefore, the number of students who like to play both the games is 10.
