(a) For x, y ER, we say ~ y if x - y ≤ 2. (b) For m, n = Z, we say m ~ n if m | n. Again, it stands for “m divides n". (c) For (x₁, y₁), (x2, Y2) € R², we say (x₁, y₁) x2 + 2y2. (d) For x, y = R, we say x~ y if x 1. Y = (x2, y2) if x₁ + 2y1 =

(a) For x, y ER, we say ~ y if x - y ≤ 2. (b) For m, n = Z, we say m ~ n if m | n. Again, it stands for “m divides n". (c) For (x₁, y₁), (x2, Y2) € R², we say (x₁, y₁) x2 + 2y2. (d) For x, y = R, we say x~ y if x 1. Y = (x2, y2) if x₁ + 2y1 =

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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Question

For each of the following, is ~ reflexive? Symmetric? Transitive? If not, provide a counterexample.

-------

This means that you do not need to give a proof if ~ is actually reflexive/symmetric/transitive. You only have to give counterexamples in case ~ is not reflexive/symmetric/transitive.

(a) For x, y = R, we say x~ y if x - y ≤ 2.
(b) For m, n = Z, we say m ~ n if m | n. Again, it stands for "m divides
n”.
(c) For (x₁, y₁), (x2, Y2) € R², we say (x₁, y₁)
x₂ + 2y₂.
(d) For x, y = R, we say x ~ y if X
=
Y
1.
(x2, y2) if x₁ + 2y₁
=

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