R is the relation on R given by a R b if a < b. Which of these describes R?

Relations & Functions · Question 13 of 125

Question 13

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$R$ is the relation on $\mathbb{R}$ given by $a \mathrel{R} b$ if $a < b$ . Which of these describes $R$ ?

Reflexive and transitive, but not symmetricCorrect answerYour answerSymmetric and transitive, but not reflexiveCorrect answerYour answerTransitive onlyCorrect answerYour answerNeither reflexive, symmetric nor transitiveCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$a < a$ is false, so it is not reflexive; $1 < 2$ but not $2 < 1$ , so not symmetric.
$a < b$ and $b < c$ give $a < c$ : it is transitive.

Worth noting

Unlike $\le$ , the strict $<$ never relates a number to itself.

Concept: Testing a relation given by a rule
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsTypes of relations

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RRR is the relation on R\mathbb{R}R given by aRba \mathrel{R} baRb if a<ba < ba<b. Which of these describes RRR?

Explanation

$R$ is the relation on $\mathbb{R}$ given by $a \mathrel{R} b$ if $a < b$ . Which of these describes $R$ ?