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Relations & Functions · Question 62 of 125

How many ordered pairs does this remainder relation R contain?

Question 62

MediumOriginal question

On A={1,2,3,4,5,6}A = \{1, 2, 3, 4, 5, 6\}, the relation RR is aRba \mathrel{R} b if a−ba - b is divisible by 3.

How many ordered pairs does this remainder relation RR contain?

Options for question 62

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. Each class has 2 elements and gives 2×2=42 \times 2 = 4 pairs.

  2. 3 classes: 3×4=123 \times 4 = 12 pairs.

Worth noting

6 counts only the pairs (a,a)(a, a).

Concept
Pairs in an equivalence relation from its classes
Typical time
120 s
Your time
—
The rule this testsEquivalence relations and classes
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Ten questions from Relations & Functions, at your own pace.

Practise this chapter →

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