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y) ∈ R mean

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 11E: Let be a relation defined on the set of all integers by if and only if sum of and is odd. Decide...

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Question

Let A = {4, 5, 6} and B = {5, 6, 7} and define relations R,
S, and T from A to B as follows:
For all (x, y) ∈ A × B,
(x, y) ∈ R means that x ≥ y.
(x, y) ∈ S means that x − y
2 is an integer.
T = {(4, 7), (6, 5), (6, 7)}.
a. Draw arrow diagrams for R, S, and T .
b. Indicate whether any of the relations R, S, and T are
functions.

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