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Question
In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find:
how many can speak both Hindi and English:
Solution
Let A & B denote the sets of the persons who like Hindi & English, respectively.
\[\text{ Given }: \]
\[n\left( A \right) = 750\]
\[n\left( B \right) = 460\]
\[n\left( A \cup B \right) = 950\]
\[\text{ We know }: \]
\[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ \Rightarrow 950 = 750 + 460 - n\left( A \cap B \right)\]
\[ \Rightarrow n\left( A \cap B \right) = 260\]
\[\text{ Thus, 260 persons can speak both Hindi and English } . \]
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