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S is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, rRy if and only y-x>0. Determine whether R is an equivalence relation, a partial ordering, or neither.

S is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, rRy if and only y-x>0. Determine whether R is an equivalence relation, a partial ordering, or neither.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Let R and S be equivalence relations on a set A; recall that by definition R, SCAXA. Prove that ROS is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, r Ry if and only y-x > 0. Determine whether R is an equivalence relation, a partial ordering, or neither. 3. Let A = {armadillo, bear, crocodile,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,
Transcribed Image Text:1. Let R and S be equivalence relations on a set A; recall that by definition R, SCAXA. Prove that ROS is an equivalence relation. 2. Define the relation R on Z as follows: for x, y E Z, r Ry if and only y-x > 0. Determine whether R is an equivalence relation, a partial ordering, or neither. 3. Let A = {armadillo, bear, crocodile,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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