Solved: Each of the following is a relation on {0, 1, 2, 3}. Draw directed graphs for

Chapter 8, Problem 1

(choose chapter or problem)

Each of the following is a relation on {0, 1, 2, 3}. Draw directed graphs for each relation, and indicate which relations are antisymmetric.

a. \(R_{1}\) = {(0, 0), (0, 2), (1, 0), (1, 3), (2, 2), (3, 0), (3, 1)}

b. \(R_{2}\) = {(0, 1), (0, 2), (1, 1), (1, 2), (1, 3), (2, 2), (3, 2)}

c. \(R_{3}\) = {(0, 0), (0, 3), (1, 0), (1, 3), (2, 2), (3, 3), (3, 2)}

d. \(R_{4}\) = {(0, 0), (1, 0), (1, 2), (1, 3), (2, 0), (2, 1), (3, 2), (3, 0)}

Text Transcription:

R_1

R_2

R_3

R_4