State whether or not each of the following is an equivalence relation on the set of vertices of an arbitrary graph. In each case give a proof or a counterexample. i. uv if there is an edge between u and v. ii. uv if there is no edge between u and v. iii. uv if there is a path between u and v.
State whether or not each of the following is an equivalence relation on the set of vertices of an arbitrary graph. In each case give a proof or a counterexample. i. uv if there is an edge between u and v. ii. uv if there is no edge between u and v. iii. uv if there is a path between u and v.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 6TFE: Label each of the following statements as either true or false. Let R be a relation on a nonempty...
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