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

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

It is not reflexive, since $(1, 1)$ is missing.
It is not symmetric, since $(1, 2)$ is in $R$ but $(2, 1)$ is not, and not transitive, since $(1, 2)$ and $(2, 3)$ are in $R$ but $(1, 3)$ is not.

Worth noting

Check transitivity with care: it is not transitive, since $(1, 2)$ and $(2, 3)$ are in $R$ but $(1, 3)$ 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),(2,3)}R = \{(1, 2), (2, 3)\}R={(1,2),(2,3)} is a relation on A={1,2,3}A = \{1, 2, 3\}A={1,2,3}. Which of these describes RRR?

Explanation

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