If A1- A2- A100 are sets such that nAi - i - 2- A1- A2- A3-A100 and -i-3100Ai-A- then nA-

The correct option is B 5 We have n(A_i)=i+2 ∴ n(A_1)=3, nbsp; n(A_2)=4, nbsp; n(A_3)=5 Similarly n(A_100)=102 given nbsp; A_1⊂ ...

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Standard XII

Mathematics

Properties of Set Operation

If A1, A2,....

Question

If $A_{1}, A_{2}, . . ., A_{100}$ are sets such that $n (A_{i}) = i + 2,$ $A_{1} \subset A_{2} \subset A_{3} . . . . . . . . A_{100}$ and $⋂_{i = 3}^{100} A_{i} = A,$ then $n (A) =$

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Solution

The correct option is B $5$
We have $n (A_{i}) = i + 2$
$∴ n (A_{1}) = 3, n (A_{2}) = 4, n (A_{3}) = 5$
Similarly $n (A_{100}) = 102$
given $A_{1} \subset A_{2} \subset A_{3} . . . . . . . . \subset A_{100}$
As $A_{3}$ is a subset of all the successive sets
$∴ A_{3} \cap A_{4} \cap A_{5} \cap . . . . . . . . \cap A_{100} = A_{3}$
$∴ A_{3} = A$
$∴ n (A) = n (A_{3}) = 5$

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If A1,A2,...,A100 are sets such that n(Ai)=i+2, A1⊂A2⊂A3........A100 and ⋂100i=3Ai=A, then n(A)=

The correct option is B 5We have n(Ai)=i+2∴n(A1)=3,n(A2)=4,n(A3)=5Similarly n(A100)=102given A1⊂A2⊂A3........⊂A100As A3 is a subset of all the successive sets∴A3∩A4∩A5∩........∩A100=A3∴A3=A∴n(A)=n(A3)=5

If $A_{1}, A_{2}, . . ., A_{100}$ are sets such that $n (A_{i}) = i + 2,$ $A_{1} \subset A_{2} \subset A_{3} . . . . . . . . A_{100}$ and $⋂_{i = 3}^{100} A_{i} = A,$ then $n (A) =$