On Z, the relation R is a R b if | a | = | b |. Which of these describes R?

Question 9

EasyOriginal question

On $\mathbb{Z}$ , the relation $R$ is $a \mathrel{R} b$ if $\lvert a \rvert = \lvert b \rvert$ . Which of these describes $R$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Equality of $\lvert a \rvert$ and $\lvert b \rvert$ is reflexive and symmetric.
If $\lvert a \rvert = \lvert b \rvert$ and $\lvert b \rvert = \lvert c \rvert$ , then $\lvert a \rvert = \lvert c \rvert$ : transitive.

Worth noting

A relation that says two things have equal values of something is always an equivalence.

Concept: Testing a relation given by a rule
Typical timeTypical: 60 s
Your timeYours: —

The rule this testsTypes of relations

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

On Z\mathbb{Z}Z, the relation RRR is aRba \mathrel{R} baRb if ∣a∣=∣b∣\lvert a \rvert = \lvert b \rvert∣a∣=∣b∣. Which of these describes RRR?

Explanation

On $\mathbb{Z}$ , the relation $R$ is $a \mathrel{R} b$ if $\lvert a \rvert = \lvert b \rvert$ . Which of these describes $R$ ?