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

Reflexive and symmetric, but not transitiveCorrect answerYour answerReflexive, symmetric and transitiveCorrect answerYour answerSymmetric and transitive, but not reflexiveCorrect answerYour answerReflexive and transitive, but not symmetricCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

It is reflexive, since every $(a, a)$ is in $R$ .
It is symmetric, since each pair's reverse is in $R$ , and transitive, since no pairs $(a, b), (b, c)$ in $R$ lack $(a, c)$ .

Worth noting

Check transitivity with care: it is transitive, since no pairs $(a, b), (b, c)$ in $R$ lack $(a, c)$ .

Concept: Testing a relation on a finite set
Typical timeTypical: 60 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),(1,2),(2,1)}R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)\}R={(1,1),(2,2),(3,3),(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

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