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

Reflexive, symmetric and transitiveCorrect answerYour answerSymmetric onlyCorrect answerYour answerReflexive and symmetric, but not transitiveCorrect answerYour answerReflexive onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

It is reflexive, since every $(a, a)$ is in $R$ .
It is symmetric, since each pair's reverse is in $R$ , 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={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)}R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (2, 3), (3, 2)\}R={(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)} is a relation on A={1,2,3}A = \{1, 2, 3\}A={1,2,3}. Which of these describes RRR?

Explanation

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