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

Relations & Functions · Question 6 of 125

Question 6

EasyOriginal question

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

Reflexive and transitive, but not symmetricCorrect answerYour answerReflexive, symmetric and transitiveCorrect answerYour answerTransitive onlyCorrect answerYour answerReflexive onlyCorrect answerYour answer

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CorrectNot quiteAnswer A

Correct answer: A

$a \le a$ always, and $a \le b$ , $b \le c$ give $a \le c$ .
But $1 \le 2$ while $2 \le 1$ is false, so it is not symmetric.

Worth noting

One counter-example, such as 1 and 2, is enough to rule out symmetry.

Concept: Testing a relation given by a rule
Typical timeTypical: 60 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 \le ba≤b. Which of these describes RRR?

Explanation

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