Define the following relations on A = {0, 1,2,4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R¡ and R2 are reflexive, simply enter 1, 2 as the answer. Ro = {(4,2), (4, 4), (4, 0), (0, 2), (0, 1), (4, 1)} R1 : {(4,4), (0,0), (1, 1), (2, 2)} R2 = {(4,4), (2,0), (2, 2), (1, 4), (2, 1), (0,0)} R3 = {(2,2), (1,0), (0, 0), (1, 1), (0, 1), (4, 4)} R4 = {(4,4), (2,0), (2, 1), (1,2), (1, 4), (4, 1), (0, 2)} 1) Which relations are reflexive? 1 2) Which relations are symmetric? 4 3) Which relations are anti-symmetric? 3 4) Which relations are transitive?
Define the following relations on A = {0, 1,2,4}. Answer each of the following questions by listing the index of the relation. For example, for Part 1), if R¡ and R2 are reflexive, simply enter 1, 2 as the answer. Ro = {(4,2), (4, 4), (4, 0), (0, 2), (0, 1), (4, 1)} R1 : {(4,4), (0,0), (1, 1), (2, 2)} R2 = {(4,4), (2,0), (2, 2), (1, 4), (2, 1), (0,0)} R3 = {(2,2), (1,0), (0, 0), (1, 1), (0, 1), (4, 4)} R4 = {(4,4), (2,0), (2, 1), (1,2), (1, 4), (4, 1), (0, 2)} 1) Which relations are reflexive? 1 2) Which relations are symmetric? 4 3) Which relations are anti-symmetric? 3 4) Which relations are transitive?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter1: Expressions And Functions
Section1.6: Relations
Problem 2AGP
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Transcribed Image Text:Define the following relations on A = {0, 1,2, 4}.
Answer each of the following questions by listing the
index of the relation. For example, for Part 1), if R1 and
R2 are reflexive, simply enter 1, 2 as the answer.
Ro = {(4, 2), (4, 4), (4, 0), (0, 2), (0, 1), (4, 1)}
R1 = {(4,4), (0, 0), (1, 1), (2, 2)}
R2 = {(4, 4), (2, 0), (2, 2), (1,4), (2, 1), (0,0)}
R3 = {(2,2), (1,0), (0,0), (1, 1), (0, 1), (4, 4)}
R4
{(4, 4), (2,0), (2, 1), (1, 2), (1,4), (4, 1), (0, 2)}
1) Which relations are reflexive?
1
2) Which relations are symmetric?
4
3) Which relations are anti-symmetric?
3
4) Which relations are transitive?
2
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