$R = \{(1, 2), (2, 3)\}$ is a relation on $A = \{1, 2, 3\}$ . What is the least number of pairs that must be added to $R$ to make it an equivalence relation?

3

Correct answerYour answer

5

Correct answerYour answer

6

Correct answerYour answer

7

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

Add the 3 pairs $(a, a)$ , then whatever the chains and reverses force.
The pairs added: $(1, 1), (1, 3), (2, 1), (2, 2), (3, 1), (3, 2), (3, 3)$ , 7 in all.

Worth noting

3 adds only the pairs $(a, a)$ ; the chains still need their missing links.

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

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

R={(1,2),(2,3)}R = \{(1, 2), (2, 3)\}R={(1,2),(2,3)} is a relation on A={1,2,3}A = \{1, 2, 3\}A={1,2,3}. What is the least number of pairs that must be added to RRR to make it an equivalence relation?