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Questions › DSE › DSE 2014 › Q29
2 marks, −0.666666666666667Mathematics › Sets, relations and functions › Sets and set operationsHardabout 2 min

DSE 2014 Question 29: Sets, relations and functions

Suppose AjA_jAj​, j=1,2,…j=1,2,\dotsj=1,2,… are non-empty sets of real numbers. Define Cn=⋂k=n∞⋃j=k∞AjC_n=\bigcap_{k=n}^{\infty}\bigcup_{j=k}^{\infty}A_jCn​=⋂k=n∞​⋃j=k∞​Aj​, n=1,2,…n=1,2,\dotsn=1,2,…. Which of the following must hold for a given nnn?

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Suppose Aⱼ, j=1,2,… are non-empty sets of real numbers. Define Cₙ=⋂ₖ₌ₙ^∞⋃ⱼ₌ₖ^∞Aⱼ, n=1,2,…. Which of the following must hold for a given n? (A) Cₙ⊂ Cₙ₊₁ (B) Cₙ₊₁⊂ Cₙ (C) Cₙ=Cₙ₊₁ (D) None of the above need hold

Also written as: Suppose A_j, j=1,2,... are non-empty sets of real numbers. Define C_n= intersection_(k=n)^(inf) union_(j=k)^(inf)A_j, n=1,2,.... Which of the following must hold for a given 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 DSE 2014 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.