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Relations & Functions · Question 7 of 125

Which of these describes this four-pair relation R?

Question 7

EasyOriginal question

On A={1,2,3}A = \{1, 2, 3\}, the relation R={(1,1),(2,2),(3,3),(2,3)}R = \{(1, 1), (2, 2), (3, 3), (2, 3)\}.

Which of these describes this four-pair relation RR?

Options for question 7

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. It is reflexive, since every (a,a)(a, a) is in RR.

  2. It is not symmetric, since (2,3)(2, 3) is in RR but (3,2)(3, 2) is not, and transitive, since no pairs (a,b),(b,c)(a, b), (b, c) in RR lack (a,c)(a, c).

Worth noting

Symmetry fails on the one pair that is not of the form (a,a)(a, a).

Concept
Testing a relation on a finite set
Typical time
90 s
Your time
—
The rule this testsTypes of relations
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Ten questions from Relations & Functions, at your own pace.

Practise this chapter →

Ten questions from Relations & Functions, at your own pace.