On $A = \{1, 3, 5\}$ , the relation $R = \{(1, 1), (1, 3), (3, 1), (3, 3)\}$ . Which of these describes $R$ ?

Reflexive, symmetric and transitiveCorrect answerYour answerSymmetric and transitive, but not reflexiveCorrect answerYour answerTransitive onlyCorrect answerYour answerSymmetric onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

It is not reflexive, since $(5, 5)$ is missing.
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 reflexivity with care: it is not reflexive, since $(5, 5)$ is missing.

Concept: Testing a relation on a finite set
Typical timeTypical: 90 s
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The rule this testsTypes of relations

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

On A={1,3,5}A = \{1, 3, 5\}A={1,3,5}, the relation R={(1,1),(1,3),(3,1),(3,3)}R = \{(1, 1), (1, 3), (3, 1), (3, 3)\}R={(1,1),(1,3),(3,1),(3,3)}. Which of these describes RRR?

Explanation

On $A = \{1, 3, 5\}$ , the relation $R = \{(1, 1), (1, 3), (3, 1), (3, 3)\}$ . Which of these describes $R$ ?