Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R). Show that: (a) If A is countable, then so does R+ S. (b) but R+S is countable. Show that the converse does not hold; that is, give an example of a set A that is uncountable

Let A be a set and R and S be relations on A. Define the relation R+S on A by R+S = (R – S)U(S – R). Show that: (a) If A is countable, then so does R+ S. (b) but R+S is countable. Show that the converse does not hold; that is, give an example of a set A that is uncountable

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

Let A be a set and R and S be relations on A. Define the relation R+ S on A by
R+S = (R – S)U (S – R).
-
Show that:
(a)
If A is countable, then so does R+ S.
Show that the converse does not hold; that is, give an example of a set A that is uncountable
(b)
but R+ S is countable.
(c)
Prove or disprove: If R and S are partial orders on A, then so does R+ S.

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