R is the relation on Z given by a R b if a - b is divisible by 4. Which of these describes R?

Question 2

EasyOriginal question

$R$ is the relation on $\mathbb{Z}$ given by $a \mathrel{R} b$ if $a - b$ is divisible by 4. Which of these describes $R$ ?

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

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

$a - a = 0$ is divisible by 4; if 4 divides $a - b$ it divides $b - a$ .
If 4 divides $a - b$ and $b - c$ , it divides their sum $a - c$ .

Worth noting

Transitivity follows by adding the two differences.

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 Z\mathbb{Z}Z given by aRba \mathrel{R} baRb if a−ba - ba−b is divisible by 4. Which of these describes RRR?

Explanation

$R$ is the relation on $\mathbb{Z}$ given by $a \mathrel{R} b$ if $a - b$ is divisible by 4. Which of these describes $R$ ?