4. Check if the following relations are partial order, or equivalence, or none. For the equivalence relations, find equivalence classes and par- tition, for partial orders, draw a Hasse diagram. (i) A= {a, b, c, d, e, f}, RA = {[a, a], [b, b], [c, c], [d, d], [e, e], [f, f], [c, d], [f, c], [d, f], [c, f], [d, c], [f, d]}, (ii) B={a, b, c, d, e, f}, RB={[a, a], [b, b], [c, c], [d, d], [e, e], [f, ƒ], [c, a], [b, a], [b, f], [c, d], [c, b], [a, d, f, d], [c, f}.

4. Check if the following relations are partial order, or equivalence, or none. For the equivalence relations, find equivalence classes and par- tition, for partial orders, draw a Hasse diagram. (i) A= {a, b, c, d, e, f}, RA = {[a, a], [b, b], [c, c], [d, d], [e, e], [f, f], [c, d], [f, c], [d, f], [c, f], [d, c], [f, d]}, (ii) B={a, b, c, d, e, f}, RB={[a, a], [b, b], [c, c], [d, d], [e, e], [f, ƒ], [c, a], [b, a], [b, f], [c, d], [c, b], [a, d, f, d], [c, f}.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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