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Relations & Functions · Question 57 of 125

Question 57

MediumOriginal question

Into how many equivalence classes does the relation 'a−ba - b is divisible by 9' split Z\mathbb{Z}?

Options for question 57

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. Two integers are related exactly when they leave the same remainder.

  2. There are 9 possible remainders, so 9 classes.

Worth noting

Each remainder 0 to 8 is one class, so there are 9, not 8.

Concept
The number of classes
Typical time
90 s
Your time
—
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.