Suppose $A_{1}, A_{2}, . . . . . . . . . . . . . . . A_{30}$ are thirty sets each having $5$ elements and $B_{1}, B_{2}, . . . . . . . . . . . . . . . B_{5}$ are $5$ sets each with $3$ elements. No element in $A$ is common with $B$ and all are distinct elements in set $A$ and set $B$ . Then, $n (A \cup B) =$

150

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15

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165

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0

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Solution

The correct option is C $165$
Each $A_{i}$ has $5$ elements i.e. $n (A_{i}) = 5$ for $i = 1, 2, . . .30$
Each $B_{i}$ has $5$ elements i.e. $n (B_{i}) = 3$ for $i = 1, 2, . . .5$
$n (⋃_{i = 1}^{30} A_{i}) = 30 \times 5 = 150$
$n (⋃_{j = 1}^{5} B_{j}) = 3 \times 5 = 15$
$n (A \cup B) = n (A) + n (B) = 150 + 15 = 165$

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