How many equivalence relations are there on $\{1, 2, 3\}$ ?

3

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5

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6

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8

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Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

An equivalence relation is the same as a split of the set into classes.
$\{1, 2, 3\}$ ; $\{1, 2\}, \{3\}$ ; $\{1, 3\}, \{2\}$ ; $\{2, 3\}, \{1\}$ ; $\{1\}, \{2\}, \{3\}$ : 5 in all.

Worth noting

3 counts only the splits into a pair and a single; the whole set and three singles are splits too.

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

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

How many equivalence relations are there on {1,2,3}\{1, 2, 3\}{1,2,3}?