R1 = {(x,y)| x + y > 10}
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:7. Consider the following relations on the set of positive integers.
R1 = {(x,y)| x + y > 10}
R2 = {(x,y)| y divides x}
R3 = {(x, y)| gcd(x, y) = 1)}
R4 = {(x,y)| x and y have the same prime divisors }
ニ
Which of these relations are reflexive, symmetric, antisymmetric or transitive? Justify your
answer.
8. Suppose A is the set composed of all ordered pairs of positive integers. Let R be the the relation
defined on A where (a, b) R(c, d) means that ad = bc. Show that R is an equivalence relation.
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