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Question

If $A subscript 1 end subscript comma A subscript 2 end subscript comma horizontal ellipsis comma A subscript 100 end subscript$ are sets such that $n open parentheses A subscript i end subscript close parentheses equals i plus 2 comma A subscript 1 end subscript subset of A subscript 2 end subscript subset of A subscript 3 end subscript horizontal ellipsis subset of A subscript 100 end subscript$ and $not stretchy ⋂ from i equals 3 to 100 of A subscript i end subscript equals A comma$ then $n open parentheses A close parentheses equals$

3
4
5
6

The correct answer is: 5

It is given that $A subscript 1 end subscript subset of A subscript 2 end subscript subset of A subscript 3 end subscript subset of horizontal ellipsis subset of A subscript 100 end subscript$
$therefore not stretchy ⋃ from i equals 3 to 100 of A subscript i end subscript equals A rightwards double arrow A subscript 3 end subscript equals A rightwards double arrow n open parentheses A close parentheses equals n open parentheses A subscript 3 end subscript close parentheses equals 3 plus 2 equals 5$

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