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

Neither reflexive, symmetric nor transitiveCorrect answerYour answerTransitive onlyCorrect answerYour answerReflexive and transitive, but not symmetricCorrect answerYour answerSymmetric and transitive, but not reflexiveCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

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 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: 120 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),(2,4),(1,4)}R = \{(1, 2), (2, 4), (1, 4)\}R={(1,2),(2,4),(1,4)} 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

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