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Question
Let A and B be two sets that \[n \left( A \right) = 16, n \left( B \right) = 14, n \left( A \cup B \right) = 25\] Then, \[n \left( A \cap B \right)\]
Options
(a) 30
(b) 50
(c) 5
(d) none of these
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Solution
We know:
\[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
Now,
\[n\left( A \cap B \right) = n\left( A \right) + n\left( B \right) - n(A \cup B)\]
= 16 + 14 \[-\] 25
= 5
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