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Relations & Functions · Question 21 of 125

Question 21

MediumOriginal question

R={(3,3)}R = \{(3, 3)\} is a relation on A={1,2,3}A = \{1, 2, 3\}. Which of these describes RR?

Options for question 21

Show the answer and explanation
CorrectNot quiteAnswer A

Correct answer: A

Explanation

  1. It is not reflexive, since (1,1)(1, 1) is missing.

  2. It is symmetric, since each pair's reverse is in RR, and transitive, since no pairs (a,b),(b,c)(a, b), (b, c) in RR lack (a,c)(a, c).

Worth noting

Check reflexivity with care: it is not reflexive, since (1,1)(1, 1) is missing.

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.