If n(Ax)=x+1 and A1 ⊂A2 ⊂A3 ⊂………⊂A99, then n[⋃x=1^99 Ax]= (1) 99 (2) 98 (3) 100 (4) 101

Name: Problem 9, Chapter 6: The IIT Foundation series of Mathematics Class
Uploaded: 2021-07-31T19:07:41-08:00
Duration: 2 min
Channel: Saurabh Chandra
Description: If n(Ax)=x+1 and A1 ⊂A2 ⊂A3 ⊂………⊂A99, then n[⋃x=1^99 Ax]= (1) 99 (2) 98 (3) 100 (4) 101

step 1 Hello students in this problem the number of elements in the set a x is given to be x plus 1 And

Question

If $\mathrm{n}\left(\mathrm{A}_{x}\right)=\mathrm{x}+1$ and $\mathrm{A}_{1} \subset \mathrm{A}_{2} \subset \mathrm{A}_{3} \subset \ldots \ldots \ldots \subset \mathrm{A}_{99}$, then $\mathrm{n}\left[\bigcup_{\mathrm{x}=1}^{99} \mathrm{~A}_{\mathrm{x}}\right]=$ (1) 99 (2) 98 (3) 100 (4) 101

    If $\mathrm{n}\left(\mathrm{A}_{x}\right)=\mathrm{x}+1$ and $\mathrm{A}_{1} \subset \mathrm{A}_{2} \subset \mathrm{A}_{3} \subset \ldots \ldots \ldots \subset \mathrm{A}_{99}$, then $\mathrm{n}\left[\bigcup_{\mathrm{x}=1}^{99} \mathrm{~A}_{\mathrm{x}}\right]=$
(1) 99
(2) 98
(3) 100
(4) 101

The IIT Foundation series of Mathematics Class

Trishna Knowledge… 5th Edition

Chapter 6, Problem 9

Instant Answer

Solved by Expert Saurabh Chandra

07/31/2021

Step 1

Step 1: Given that the number of elements in the set $\mathrm{A}_{x}$ is $\mathrm{x}+1$ and $\mathrm{A}_{1} \subset \mathrm{A}_{2} \subset \mathrm{A}_{3} \subset \ldots \subset \mathrm{A}_{99}$, we need to find the number of elements in the union of all these sets. Show more…

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If $\mathrm{n}\left(\mathrm{A}_{x}\right)=\mathrm{x}+1$ and $\mathrm{A}_{1} \subset \mathrm{A}_{2} \subset \mathrm{A}_{3} \subset \ldots \ldots \ldots \subset \mathrm{A}_{99}$, then $\mathrm{n}\left[\bigcup_{\mathrm{x}=1}^{99} \mathrm{~A}_{\mathrm{x}}\right]=$ (1) 99 (2) 98 (3) 100 (4) 101

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Key Concepts

Union of Sets

The union of sets is the set that contains all the elements from each of the involved sets. When dealing with nested sets, the union is equivalent to the largest set because it already includes all elements from the preceding subsets.

Nested Sets

This concept refers to a sequence of sets where each set is contained within the following one. In such a structure, the union of these nested sets is simply the largest set in the sequence, since every other set's elements are included in it.

Cardinality

Cardinality is the measure of the number of elements in a set. When sets are nested, the cardinality of the union equals the cardinality of the largest set, as it encompasses all the elements from the smaller sets.

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