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Question
If A and B are two sets such that \[n \left( A \right) = 20, n \left( B \right) = 25\]\text{ and } \[n \left( A \cup B \right) = 40\], then write \[n \left( A \cap B \right)\]
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Solution
We have:
\[n\left( A \right) = 20, n\left( B \right) = 25 \text{ and } n\left( A \cup B \right) = 40\]
We know:
\[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ \Rightarrow n\left( A \cap B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cup B \right)\]
= 20 + 25
\[-\] 40
= 5
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