a) Let R be a binary relation on the set of integers such that (a,b) ER if and only if b = 2a. What is the composite relation RoR? b) Let R be a binary relation on the set of ordered pairs of integers such that ((a,b),(c,d)) ER if and only if ad = bc. Show that R is an equivalence relation.

a) Let R be a binary relation on the set of integers such that (a,b) ER if and only if b = 2a. What is the composite relation RoR? b) Let R be a binary relation on the set of ordered pairs of integers such that ((a,b),(c,d)) ER if and only if ad = bc. Show that R is an equivalence relation.

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

a)
Let R be a binary relation on the set of integers such that (a,b) ER if and only if b = 2a.
What is the composite relation RoR?
b)
Let R be a binary relation on the set of ordered pairs of integers such that ((a,b), (c,d)) E R
if and only if ad = bc. Show that R is an equivalence relation.

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