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

Symmetric onlyCorrect answerYour answerSymmetric and transitive, but not reflexiveCorrect answerYour answerReflexive and symmetric, but not transitiveCorrect answerYour answerNeither reflexive, symmetric nor transitiveCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

It is not reflexive, since $(1, 1)$ is missing.
It is symmetric, since each pair's reverse is in $R$ , and not transitive, since $(1, 2)$ and $(2, 1)$ are in $R$ but $(1, 1)$ is not.

Worth noting

Check transitivity with care: it is not transitive, since $(1, 2)$ and $(2, 1)$ are in $R$ but $(1, 1)$ is not.

Concept: Testing a relation on a finite set
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsTypes of relations

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

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

Explanation

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