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Questions › DSE › DSE 2011 › Q30
2 marksMathematics › Real analysis › Topology of the real line: open, closed and compact setsHardabout 4 min

DSE 2011 Question 30: Real analysis

Setup, from Q27 of the paper:

Consider a Society of individuals who may belong to sets called Clubs and Tribes, satisfying: the entire Society is a Tribe; the empty subset is a Tribe; the intersection of any collection of Tribes is a Tribe; the union of any two Tribes is a Tribe; a set is a Club if and only if the set of individuals not in it is a Tribe. The intersection of two Clubs is necessarily

(Same Clubs-and-Tribes setup.) Given a Club and a Tribe, the set of individuals who belong to the given Tribe but not to the given Club necessarily constitute

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Answer and worked solution

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Real analysis has come up 38 times in 5 exams since 2005.

What this question tests

This question is on Topology of the real line: open, closed and compact sets, part of Real analysis in Mathematics.

Which sets are open, closed or compact and how unions and intersections behave.

TestStop has 29 past-paper questions on this subtopic.

Practise Real analysisMore on Topology of the real line: open, closed and compact sets

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Question from the DSE 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.