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Question
Let U be the universal set containing 700 elements. If A, B are sub-sets of U such that \[n \left( A \right) = 200, n \left( B \right) = 300 \text{ and } \left( A \cap B \right) = 100\].Then \[n \left( A' \cap B' \right) =\]
Options
(a) 400
(b) 600
(c) 300
(d) none of these.
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Solution
(c) 300
n( \[A' \cap B'\]) = \[n\left( A \cup B \right)'\]
\[= n\left( U \right) - n(A \cup B)\]
\[ = 700 - \left\{ 200 + 300 - 100 \right\}\]
\[ = 300\]
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