4. Consider the following binary relation p on the plane R² (x, y)p(u, v) if y? – a² = v² – u². Prove that p is an equivalence relation. Describe the corresponding partition of R². Justify.
4. Consider the following binary relation p on the plane R² (x, y)p(u, v) if y? – a² = v² – u². Prove that p is an equivalence relation. Describe the corresponding partition of R². Justify.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 12E: Let and be lines in a plane. Decide in each case whether or not is an equivalence relation, and...
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