Which of these describes this remainder…

Which of these describes this remainder relation R on A?

Question 49

EasyOriginal question

On $A = \{1, 2, 3, 4, 5, 6\}$ , the relation $R$ is $a \mathrel{R} b$ if $a - b$ is divisible by 3.

Which of these describes this remainder relation $R$ on $A$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

$a - a = 0$ is divisible by 3, and if 3 divides $a - b$ it divides $b - a$ .
If 3 divides $a - b$ and $b - c$ , it divides $a - c$ : an equivalence relation.

Worth noting

Adding the two differences proves transitivity.

Concept: Recognising an equivalence relation
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsEquivalence relations and classes

Practise this chapter →

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

Practise this chapter →

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

Which of these describes this remainder relation R on A?

Question 49

Explanation