First slide

Operations on Sets

Question

In a class of 60 students, 25 students play cricket and 20 play tennis. If 10 students play both the games, then the number of students who play neither game is _.

Moderate

Solution

$\begin{aligned} G i v e n n (U) = 60, n (C) = 25, n (T) = 20, n (C \cap T) = 10 \\ \begin{aligned} n (C^{'} \cap T) & = n (C \cup T)^{'} \\ = n (U) - n (C \cup T) \\ = n (U) - [n (C) + n (T) - n (C \cap T)] \\ = 60 - [25 + 20 - 10] \\ = 25 \end{aligned} \end{aligned}$

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