Need help with 1 1. Let R and S be equivalence relations on a set A; recall that by definitionR,SCAX A. Prove that RAS is an equivalence relation.2. Define the relation Ron Z as follows: for r, y EZ, xRy if and only y –x > 0.Determine whether Ris an equivalence relation, a partial ordering, or neither.3. Let A = {armadillo, bear, erocodile,dolphin, eagle, fox}. Construct a par-tial ordering3 on A that satisfies the conditions below. (You may draw aHasse diagram to demonstrate your partial ordering.armadillo 3 eagle.The least upper bound of the set {bear, eagle, fox} is "crocodile"."fox" is a minimal element of the partial ordering.4. Given the slightly blurry Hasse diagram below, find all maximal, minimal,

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Answered: 1. Let R and S be equlvalence relations…

1. Let R and S be equlvalence relations on a set A; recall that by definition R, SCAXA. Prove that RnS is an equivalence relation.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 15E: Let A=R0, the set of all nonzero real numbers, and consider the following relations on AA. Decide in...

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Need help with 1

1. Let R and S be equivalence relations on a set A; recall that by definition
R,SCAX A. Prove that RAS is an equivalence relation.
2. Define the relation Ron Z as follows: for r, y EZ, xRy if and only y –x > 0.
Determine whether Ris an equivalence relation, a partial ordering, or neither.
3. Let A = {armadillo, bear, erocodile,dolphin, eagle, fox}. Construct a par-
tial ordering3 on A that satisfies the conditions below. (You may draw a
Hasse diagram to demonstrate your partial ordering.
armadillo 3 eagle.
The least upper bound of the set {bear, eagle, fox} is "crocodile".
"fox" is a minimal element of the partial ordering.
4. Given the slightly blurry Hasse diagram below, find all maximal, minimal,

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