# Equivalence Relations

## Homework Statement

I need a little help in understand this question:

Let E and F be two sets, R a binary relation on the set E and S a binary relation on the set F. We define a binary relation, denoted RxS, on the set ExF in the following way ("coordinate- wise"):
(a,b) (RxS) (c,d) <--> aRc and bSd.
If R and S are equivalence relations, prove that RxS is an equivalence relation.

unknown

## The Attempt at a Solution

I said aRc => (a,c) and bSd=> (b,d)

I assumed that aRc and bSd are from ExF.
I'm not sure that what I am doing is right

## Answers and Replies

vela
Staff Emeritus
Science Advisor
Homework Helper
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ExF is the set of ordered pairs (x,y) where x is in E and y is in F. You have (a,b) and (c,d) are elements in ExF, so this means a and c are elements of E while b and d are elements of F.

To show that RxS is an equivalence relation, you need to show it satisfies three properties: reflexivity, symmetry, and transitivity.

## Homework Statement

I need a little help in understand this question:

Let E and F be two sets, R a binary relation on the set E and S a binary relation on the set F. We define a binary relation, denoted RxS, on the set ExF in the following way ("coordinate- wise"):
(a,b) (RxS) (c,d) <--> aRc and bSd.
If R and S are equivalence relations, prove that RxS is an equivalence relation.

unknown

## The Attempt at a Solution

I said aRc => (a,c) and bSd=> (b,d)

I assumed that aRc and bSd are from ExF.
I'm not sure that what I am doing is right