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

Reflexive, symmetric and transitiveCorrect answerYour answerTransitive onlyCorrect answerYour answerReflexive onlyCorrect answerYour answerReflexive and transitive, but not symmetricCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

It is reflexive, since every $(a, a)$ is in $R$ .
It is not symmetric, since $(1, 3)$ is in $R$ but $(3, 1)$ is not, and transitive, since no pairs $(a, b), (b, c)$ in $R$ lack $(a, c)$ .

Worth noting

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

Explanation

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