2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation defined on Ax B such that (a, b)R(a', b') if and only if aRia' and bR₂b. Prove that if R₁ and R₂ are equivalence relations then R is also an equivalence relation.
2. Let R₁ be a relation on the set A and R₂ be a relation on the set B. Let R be the relation defined on Ax B such that (a, b)R(a', b') if and only if aRia' and bR₂b. Prove that if R₁ and R₂ are equivalence relations then R is also an equivalence relation.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.7: Relations
Problem 28E
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