4. Sets, Functions, and Relations

Equivalence Relations — Quiz

Test your understanding of equivalence relations with 5 practice questions.

Practice Questions

Question 1

Which property of a relation says that whenever $aRb$, then $bRa$?

Question 2

How many equivalence classes does the relation on $\mathbb{Z}$ defined by $aRb$ iff $a-b$ is even have?

Question 3

Which set is the equivalence class of $5$ under the relation on $\mathbb{Z}$ given by $aRb$ iff $a-b$ is divisible by $4$?

Question 4

Which collection is a partition of $\{1,2,3,4\}$ and could therefore be the set of equivalence classes of some equivalence relation?

Question 5

For the relation on $\{1,2,3\}$ given by $R=\{(1,1),(1,2),(2,1),(2,2),(3,3)\}$, which equivalence class contains $1$?