R is the relation on Z given by a R b if a - b is divisible by 4. What is the equivalence class of 0?

Question 58

MediumOriginal question

$R$ is the relation on $\mathbb{Z}$ given by $a \mathrel{R} b$ if $a - b$ is divisible by 4. What is the equivalence class of 0?

\{\ldots, -6, -2, 2, 6, 10, \ldots\}

Correct answerYour answer

\{\ldots, -8, -4, 0, 4, 8, \ldots\}

Correct answerYour answer

\{0, 4, 8, 12, \ldots\}

Correct answerYour answer

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

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The class of 0 is every integer $b$ with $0 - b$ divisible by 4: 0 plus or minus a multiple of 4.
So it runs $-8, -4, 0, 4, 8$ and on in both directions.

Worth noting

The class of 0 is the multiples of 4; the multiples of 2 also take in 2, 6 and 10, which are 2 away.

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