$R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 3)\}$ is a relation on $A = \{1, 2, 3, 4\}$ . Which of these describes $R$ ?

Reflexive and transitive, but not symmetricCorrect answerYour answerNeither reflexive, symmetric nor transitiveCorrect answerYour answerReflexive onlyCorrect answerYour answerReflexive and symmetric, but not transitiveCorrect 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 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: 120 s
Your timeYours: —

The rule this testsTypes of relations

Practise this chapter →

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

R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3)}R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 3)\}R={(1,1),(2,2),(3,3),(4,4),(1,2),(2,3)} is a relation on A={1,2,3,4}A = \{1, 2, 3, 4\}A={1,2,3,4}. Which of these describes RRR?

Explanation

$R = \{(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 3)\}$ is a relation on $A = \{1, 2, 3, 4\}$ . Which of these describes $R$ ?