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Question
If A and B are two sets such that \[n \left( A \right) = 115, n \left( B \right) = 326, n \left( A - B \right) = 47,\] then write \[n \left( A \cup B \right)\]
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Solution
\[n\left( A \right) = 115, n\left( B \right) = 326 \text{ and } n\left( A - B \right) = 47\]
\[\text{ Now }, \]
\[n\left( A \right) - n\left( A \cap B \right) = n\left( A - B \right)\]
\[ \Rightarrow 115 - n\left( A \cap B \right) = 47\]
\[ \Rightarrow n\left( A \cap B \right) = 68\]
Thus, we get:
\[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[-\] 68
= 373
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