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Elements Of Modern Algebra
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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Let A={a,b,c,d,e} and S, T, U and V relations on A where

S = {(a,a), (a,b), (b,c), (b,d), (c,e), (e,d), (c,a)}

T = {(a,b), (b,a), (b,c), (b,d), (e,e), (d,e), (c,b)}

U= {(a,b), (a,a), (b,c), (b,b), (e,e), (b,a), (c,b), (c,c), (d,d), (a,c), (c,a)}

V= {(a,b), (b,c), (b,b), (e,e), (b,a), (c,b), (d,d), (a,c), (c,a)}

a)    Which of the relations are reflexive? Justify your answer. 

b)    Which of the relations are antisymmetric? Justify your answer. 

c)    Find U  V. 

d)    Find T─S.

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