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Relations & Functions · Question 23 of 125

What is the least number of pairs to add to this four-pair R to make it an equivalence relation?

Question 23

MediumOriginal question

On A={1,2,3}A = \{1, 2, 3\}, the relation R={(1,1),(2,2),(3,3),(2,3)}R = \{(1, 1), (2, 2), (3, 3), (2, 3)\}.

What is the least number of pairs to add to this four-pair RR to make it an equivalence relation?

Options for question 23

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. It is already reflexive and transitive; it lacks only symmetry.

  2. Adding (3,2)(3, 2) is enough, and keeps it transitive: 1 pair.

Worth noting

2 also adds a pair linking 1, which nothing in RR requires.

Concept
The smallest equivalence relation containing a set of pairs
Typical time
120 s
Your time
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