R is the relation on Z given by a R b if a - b is divisible by 3. What is the equivalence class of 2?

Relations & Functions · Question 46 of 125

Question 46

EasyOriginal question

$R$ is the relation on $\mathbb{Z}$ given by $a \mathrel{R} b$ if $a - b$ is divisible by 3. What is the equivalence class of 2?

\{\ldots, -6, -3, 0, 3, 6, \ldots\}

Correct answerYour answer

\{2, 5, 8, 11, \ldots\}

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\{\ldots, -4, -2, 0, 2, 4, \ldots\}

Correct answerYour answer

\{\ldots, -4, -1, 2, 5, 8, \ldots\}

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Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The class of 2 is every integer $b$ with $2 - b$ divisible by 3: 2 plus or minus a multiple of 3.
So it runs $-4, -1, 2, 5, 8$ and on in both directions.

Worth noting

The multiples of 3 form the class of 0, not of 2.

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

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