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 28E
Related questions
Question
![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}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2889a789-6264-4928-9ca2-9b6509924020%2Fb9e1fb9a-7500-42c3-aa8a-1c180521c2db%2F0vrj9k_processed.jpeg&w=3840&q=75)
Transcribed Image Text: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}.
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