R is the relation on Z given by a R b if a - b is divisible by 5. What is the equivalence class of 3?

Question 56

MediumOriginal question

$R$ is the relation on $\mathbb{Z}$ given by $a \mathrel{R} b$ if $a - b$ is divisible by 5. What is the equivalence class of 3?

\{\ldots, -7, -2, 3, 8, 13, \ldots\}

Correct answerYour answer

\{\ldots, -10, -5, 0, 5, 10, \ldots\}

Correct answerYour answer

\{3, 8, 13, 18, \ldots\}

Correct answerYour answer

\{\ldots, -8, -3, 2, 7, 12, \ldots\}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The class of 3 is every integer $b$ with $3 - b$ divisible by 5: 3 plus or minus a multiple of 5.
So it runs $-7, -2, 3, 8, 13$ and on in both directions.

Worth noting

The class runs both ways: $-2$ and $-7$ are in it too, since $3 - (-2) = 5$ .

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