R is the relation on R given by a R b if | a - b | ≤ 1. Which of these describes R?

Question 18

MediumOriginal question

$R$ is the relation on $\mathbb{R}$ given by $a \mathrel{R} b$ if $\lvert a - b \rvert \le 1$ . Which of these describes $R$ ?

Reflexive and symmetric, but not transitiveCorrect answerYour answerReflexive, symmetric and transitiveCorrect answerYour answerSymmetric onlyCorrect answerYour answerReflexive onlyCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$\lvert a - a \rvert = 0 \le 1$ , and $\lvert a - b \rvert = \lvert b - a \rvert$ : reflexive and symmetric.
0 and 1 are related, 1 and 2 are related, but $\lvert 0 - 2 \rvert = 2 > 1$ : not transitive.

Worth noting

Small steps can add up to a big one, so 'close to' is not transitive.

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−b∣≤1\lvert a - b \rvert \le 1∣a−b∣≤1. Which of these describes RRR?

Explanation

$R$ is the relation on $\mathbb{R}$ given by $a \mathrel{R} b$ if $\lvert a - b \rvert \le 1$ . Which of these describes $R$ ?