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Question
\[\cap\] If A and B are two disjoint sets, then \[n \left( A \cup B \right)\]is equal to
Options
(a) \[n \left( A \right) + n\left( B \right)\]
(b) \[n \left( A \right) + n\left( B \right) - n\left( A \cap B \right)\]
(c)\[n \left( A \right) + n \left( B \right) + n \left( A \cap B \right)\]
(d) \[n \left( A \right) n \left( B \right)\]
(e) \[n \left( A \right) - n \left( B \right)\]
Solution
\[n \left( A \right) + n\left( B \right)\]
Two sets are disjoint if they do not have a common element in them, i.e., A \[\cap\]B = \[\varnothing\]
∴ \[n\left( A \cup B \right) = n\left( A \right) + n\left( B \right)\]
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