## Related questions with answers

Question

Explain the relationship between equivalence relations on a set and partitions of this set.

Solution

VerifiedStep 1

1 of 2A relation $R$ is an $\textbf{equivalence relation}$ if the relation $R$ is transitive, symmetric and reflexive.

A $\textbf{partition}$ of a set $S$ is a collection of $\textit{disjoint subsets}$ whose union is equal to the set $S$.

The collection of ordered pairs produced by a partition will form an equivalence relation (thus if $a$ and $b$ are elements of the same set in the partition, then $(a,b)$ is in the equivalence relation).

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Discrete Mathematics and Its Applications

7th Edition•ISBN: 9780073383095Kenneth Rosen4,283 solutions

#### Discrete Mathematics and Its Applications

8th Edition•ISBN: 9781259676512Kenneth Rosen4,397 solutions

## More related questions

1/4

1/7