Question 7 Define a relation R on the set of integers Z by: aRb if and only if ab >0 (a) Show that R is symmetric. (b) Show that R is transitive. (c) Show that R is not reflexive. (d) Which minimal set of pairs should be added to R to make it an equivalence relation, and what would the equivalence classes be for this equivalence relation?
Question 7 Define a relation R on the set of integers Z by: aRb if and only if ab >0 (a) Show that R is symmetric. (b) Show that R is transitive. (c) Show that R is not reflexive. (d) Which minimal set of pairs should be added to R to make it an equivalence relation, and what would the equivalence classes be for this 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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Transcribed Image Text:Question 7
Define a relation R on the set of integers Z by:
aRb if and only if ab > 0
(a) Show that R is symmetric.
(b) Show that R is transitive.
(c) Show that R is not reflexive.
(d) Which minimal set of pairs should be added to R to make it an
equivalence relation, and what would the equivalence classes be for this
equivalence relation?
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