a) Identify which of these relations are reflexive, which are symmetric, which are transitive, and which are equivalence relations. You do not need to show any working. i) A is the set of all animals, R1 Ax A {(a, b) | a is the same species as b} C %3D i) R2 = {(m, n) | m² < n?} CZx Z ii) R3 = {(x, y) | r+ y < 1} CR xR iv) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2,2)} CBx B v) B = {0, 1, 2}, R5 = {(0, 1), (1, 2), (2,0)} CBx B
a) Identify which of these relations are reflexive, which are symmetric, which are transitive, and which are equivalence relations. You do not need to show any working. i) A is the set of all animals, R1 Ax A {(a, b) | a is the same species as b} C %3D i) R2 = {(m, n) | m² < n?} CZx Z ii) R3 = {(x, y) | r+ y < 1} CR xR iv) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2,2)} CBx B v) B = {0, 1, 2}, R5 = {(0, 1), (1, 2), (2,0)} CBx B
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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![a) Identify which of these relations are reflexive, which are symmetric, which are
transitive,
and which are equivalence relations. You do not need to show any working.
{(a, b) | a is the same species as b} C
i) A is the set of all animals, R1
Ax A
ii) R2 = {(m, n) | m² < n?} CZx Z
ii) R3 = {(x, y) |r +y < 1} CR x R
%3D
iv) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2, 2)}CBx B
v) B = {0, 1, 2}, R, = {(0, 1), (1, 2), (2,0)} C Bx B](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9a831626-ccc1-42cc-8bf9-75286de58fba%2F4c34c36f-1d63-4f6f-b4c0-5c23e45e9a24%2Fn7c079_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Identify which of these relations are reflexive, which are symmetric, which are
transitive,
and which are equivalence relations. You do not need to show any working.
{(a, b) | a is the same species as b} C
i) A is the set of all animals, R1
Ax A
ii) R2 = {(m, n) | m² < n?} CZx Z
ii) R3 = {(x, y) |r +y < 1} CR x R
%3D
iv) B = {0, 1, 2}, R4 = {(0,0), (0, 1), (1,0), (1, 1), (2, 2)}CBx B
v) B = {0, 1, 2}, R, = {(0, 1), (1, 2), (2,0)} C Bx B
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