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Questions › JNU › JNU SSS 2021 › Q73
1 markMathematics › Sets, relations and functions › Sets and set operationsModerateabout 1 min

JNU SSS 2021 Question 73: Sets, relations and functions

A σ\sigmaσ –algebra F of subsets of X is a collection F of subsets of X hold the following conditions:

I. ∅∈F\emptyset \in F∅∈F

II. if B∈FB \in FB∈F then its complement BcB^cBc is also in F

III. if B1,B2,…B_1, B_2, \ldotsB1​,B2​,… is a countable collection of sets in F then their union ⋃n=1∞Bn\bigcup_{n=1}^{\infty} B_n⋃n=1∞​Bn​

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A σ –algebra F of subsets of X is a collection F of subsets of X hold the following conditions: I. ∅ ∈ F II. if B ∈ F then its complement B^c is also in F III. if B₁, B₂, … is a countable collection of sets in F then their union ⋃ₙ₌₁^∞ Bₙ (A) Hold I and II (B) Hold II and III (C) Hold only I (D) Hold I, II and III.

Also written as: A sigma –algebra F of subsets of X is a collection F of subsets of X hold the following conditions: I. {} in F II. if B in F then its complement B^c is also in F III. if B_1, B_2,... is a countable collection of sets in F then their union union_(n=1)^(inf) B_n

Sets, relations and functions has come up 65 times in 6 exams since 2004.

What this question tests

This question is on Sets and set operations, part of Sets, relations and functions in Mathematics.

Unions, intersections, complements and differences of sets, and the identities that connect them.

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Question from the JNU SSS 2021 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.