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Question
Let A and B be two sets having 3 and 6 elements respectively. Write the minimum number of elements that \[A \cup B\]
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Solution
\[\text{ We know that } n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
\[ n\left( A \cup B \right) \text{ is minimum when } n\left( A \cap B \right) \text{ is maximum }\]
\[so, n\left( A \cap B \right) = 3\]
\[\text{ Hence }, n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right) \]
\[ = 3 + 6 - 3\]
\[ = 6\]
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