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

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

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CorrectNot quiteAnswer A

Correct answer: A

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: 120 s
Your timeYours: —

The rule this testsTypes of relations

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

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

Explanation

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