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Questions › DSE › DSE 2020 › Q19
4 marks, −1Mathematics › Sets, relations and functions › Relations and their propertiesHardabout 4 min

DSE 2020 Question 19: Sets, relations and functions

Let ≻\succ≻ on XXX be asymmetric and negatively transitive, and define x∼yx\sim yx∼y iff ¬(x≻y)\lnot(x\succ y)¬(x≻y) and ¬(y≻x)\lnot(y\succ x)¬(y≻x). The relation ∼\sim∼ is said to be transitive if x∼yx\sim yx∼y and y∼zy\sim zy∼z imply x∼zx\sim zx∼z. Then ∼\sim∼

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Let ≻ on X be asymmetric and negatively transitive, and define x~ y iff ¬(x≻ y) and ¬(y≻ x). The relation ~ is said to be transitive if x~ y and y~ z imply x~ z. Then ~ (A) is transitive (B) is not transitive (C) may not be transitive (D) is not transitive over a nonempty subset of X

Also written as: Let >- on X be asymmetric and negatively transitive, and define x~ y iff not (x>- y) and not (y>- x). The relation ~ is said to be transitive if x~ y and y~ z imply x~ z. 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.