    0

# What are equivalence relations?

Updated: 4/28/2022 Wiki User

14y ago

An equivalence relation r on a set U is a relation that is symmetric (A r Bimplies B r A), reflexive (Ar A) and transitive (A rB and B r C implies Ar C). If these three properties are true for all elements A, B, and C in U, then r is a equivalence relation on U.

For example, let U be the set of people that live in exactly 1 house. Let r be the relation on Usuch that A r B means that persons A and B live in the same house. Then ris symmetric since if A lives in the same house as B, then B lives in the same house as A. It is reflexive since A lives in the same house as him or herself. It is transitive, since if A lives in the same house as B, and B lives in the same house as C, then Alives in the same house as C. So among people who live in exactly one house, living together is an equivalence relation.

The most well known equivalence relation is the familiar "equals" relationship. Wiki User

14y ago  Study guides

20 cards

## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

➡️
See all cards
3.81
3042 Reviews Earn +20 pts  