If A1 ⊂A2 ⊂A3 ⊂…⊂A50 and n(Ax)=x-1, then find n[⋂x=11^50 Ax]. (1) 49 (2) 50 (3) 11 (4) 10

Name: Problem 5, Chapter 6: The IIT Foundation series of Mathematics Class
Uploaded: 2021-07-31T19:03:58-08:00
Duration: 2 min 2 s
Channel: Saurabh Chandra
Description: If A1 ⊂A2 ⊂A3 ⊂…⊂A50 and n(Ax)=x-1, then find n[⋂x=11^50 Ax]. (1) 49 (2) 50 (3) 11 (4) 10

step 1 Hello students in this problem given that A1 is subset of A2 is subset of A3 and so on till set

If A1 ⊂A2 ⊂A3 ⊂…⊂A50 and n(Ax)=x-1, then find n[⋂x=11^50...

If $\mathrm{A}_{1} \subset \mathrm{A}_{2} \subset \mathrm{A}_{3} \subset \ldots \subset \mathrm{A}_{50}$ and $\mathrm{n}\left(\mathrm{A}_{\mathrm{x}}\right)=\mathrm{x}-1$, then find $\mathrm{n}\left[\bigcap_{\mathrm{x}=11}^{50} \mathrm{~A}_{\mathrm{x}}\right]$. (1) 49 (2) 50 (3) 11 (4) 10

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Key Concepts

Nested Sets

Nested sets are a sequence of sets where each set is a subset of the next. This property guarantees that all elements in an earlier set are also contained in every subsequent set. Understanding nested sets helps in recognizing that operations like intersections and unions can often be simplified by focusing on the smallest or largest set in the sequence.

Cardinality

Cardinality is a measure of the number of elements in a set. In problems involving nested sets, knowing the cardinality of each set allows you to deduce the size of intersections or unions. Cardinality is particularly useful when the sets have known sizes that follow a specific pattern, simplifying the analysis of their relationships.

Intersection of Sets

The intersection of a collection of sets consists of all elements that are common to every set in the collection. In the context of nested sets, the intersection is usually the smallest set in the chain because every element of the smallest set is guaranteed to appear in all larger sets. This concept is fundamental when determining the overlap between multiple sets with known inclusion relations.

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