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Relations & Functions · Question 30 of 125

Question 30

MediumOriginal question

On A={1,3,5}A = \{1, 3, 5\}, the relation R={(1,1),(3,3),(5,5),(1,3),(3,5)}R = \{(1, 1), (3, 3), (5, 5), (1, 3), (3, 5)\}. Which of these describes RR?

Options for question 30

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 (1,3)(1, 3) is in RR but (3,1)(3, 1) is not, and not transitive, since (1,3)(1, 3) and (3,5)(3, 5) are in RR but (1,5)(1, 5) is not.

Worth noting

Check transitivity with care: it is not transitive, since (1,3)(1, 3) and (3,5)(3, 5) are in RR but (1,5)(1, 5) is not.

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.