1. Let X be a set, R, S C X × X binary relations on X. Prove or disprove the following. (a) If R and S are equivalence relations, then RUS is an equivalence relation. (b) If R and S are equivalence relations, then RNS is 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 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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Abstract Algebra: Please do b

1. Let X be a set, R, S C X × X binary relations on X. Prove or disprove the following.
(a) If R and S are equivalence relations, then RUS is an equivalence relation.
(b) If R and S are equivalence relations, then RNS is an equivalence relation.
Transcribed Image Text:1. Let X be a set, R, S C X × X binary relations on X. Prove or disprove the following. (a) If R and S are equivalence relations, then RUS is an equivalence relation. (b) If R and S are equivalence relations, then RNS is an equivalence relation.
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