1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check whether R is an equivalence relation or a partial order. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation or a partial order.

1. Let A = {0,1,2,3} and R a relation over A: R = {(0,0).(0,1).(0,3).(1,1),(1,0).(2,3).(3,3)} Check whether R is an equivalence relation or a partial order. Give a counterexample in each case in which the relation does not satisfy one of the properties of being an equivalence relation or a partial order.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Please solve the screenshot, thank you!
Prove or disprove reflexivity, symmetry and transitivity of R.
Let A = {-1,0, 1} and R be a relation on A such that R = {(a,b)|a² = b}. Select all properties of this relation. reflexive symmetric anti-symmetric transitive equivalence relation partial order
Let R be an equivalence relation on A = {0, 1,5, 6, 8, 9} and R = {(6, 1), (1,6), (6, 6), (1, 1), (0, 0), (5, 5), (5, 8), (5,9), (8,5), (8, 8), (8, 9), (9, 5), (9, 8), (9,9)}. Show the partition of A defined by the equivalence classes of R.
Give examples of relations R and S on Z such that (a) Both R and S are not equivalence relations but R+ S is. (b) Both R and S are not partial order relations but R+ S is. Show that if both R and S are equivalences relations, then R+S is not an equivalence relation.
Which of these relations on {0, 1, 2, 3} are ?equivalence relations a) {(0, 0), (1, 1), (2, 2), (3, 3)} b) {(0, 0), (0, 2), (2, 0), (2, 2), (2, 3), (3, 2), (3, 3)} c) {(0, 0), (1, 1), (1, 2), (2, 1), (2, 2), (3, 3)} d) {(0, 0), (1, 1), (1, 3), (2, 2), (2, 3), (3, 1), (3, 2), (3,3)}