In a class of 35 students, 24 like to play cricket and 16 like to play football. Also, each student

Hindi

1.Set Theory

easy

In a class of $35$ students, $24$ like to play cricket and $16$ like to play football. Also, each student likes to play at least one of the two games. How many students like to play both cricket and football?

$5$

Solution

Let $X$ be the set of students who like to play cricket and $Y$ be the set of students who like to play football. Then $X \cup Y$ is the set of students who like to play at least one game, and $X \cap Y$ is the set of students who like to play both games.

Given $\quad n( X )=24, n( Y )=16, n( X \cup Y )=35, n( X \cap Y )=?$

Using the formula $n( X \cup Y )=n( X )+n( Y )-n( X \cap Y ),$ we get

$35=24+16-n( X \cap Y )$

Thus, $n( X \cap Y )=5$

i.e., $\quad 5$ students like to play both games.

Standard 11

Mathematics

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