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Questions › DSE › DSE 2020 › Q17
4 marks, −1Mathematics › Sets, relations and functions › Relations and their propertiesHardabout 4 min

DSE 2020 Question 17: Sets, relations and functions

Let ≻\succ≻ on XXX be asymmetric and negatively transitive. Define x⪰yx\succeq yx⪰y iff ¬(y≻x)\lnot(y\succ x)¬(y≻x). The relation ⪰\succeq⪰ is said to be total if, for all x,yx,yx,y, x⪰yx\succeq yx⪰y or y⪰xy\succeq xy⪰x. Then ⪰\succeq⪰

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Let ≻ on X be asymmetric and negatively transitive. Define x⪰ y iff ¬(y≻ x). The relation ⪰ is said to be total if, for all x,y, x⪰ y or y⪰ x. Then ⪰ (A) is not total (B) is total (C) may not be total (D) is not total over a nonempty subset of X

Also written as: Let >- on X be asymmetric and negatively transitive. Define x>-= y iff not (y>- x). The relation >-= is said to be total if, for all x,y, x>-= y or y>-= x. Then >-=

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

What this question tests

This question is on Relations and their properties, part of Sets, relations and functions in Mathematics.

Binary relations and what reflexive, symmetric, transitive, complete and order properties imply.

TestStop has 6 past-paper questions on this subtopic.

Practise Sets, relations and functionsMore on Relations and their properties

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Question from the DSE 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.