n 1-8 a number of relations are defined on the set A = {0, 1, 2, 3}. For each relation: a.) Draw the directed graph. b.) Determine whether the relation is reflexive. c.) Determine whether the relation is symmetric. d.) Determine whether the relation is transitive. Give a counterexample in each case in which the relation does not satisfy one of the properties.

n 1-8 a number of relations are defined on the set A = {0, 1, 2, 3}. For each relation: a.) Draw the directed graph. b.) Determine whether the relation is reflexive. c.) Determine whether the relation is symmetric. d.) Determine whether the relation is transitive. Give a counterexample in each case in which the relation does not satisfy one of the properties.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

In 1-8 a number of relations are defined on the set A = {0, 1, 2, 3}.
For each relation:

a.) Draw the directed graph.
b.) Determine whether the relation is reflexive.
c.) Determine whether the relation is symmetric.
d.) Determine whether the relation is transitive.

Give a counterexample in each case in which the relation does not satisfy
one of the properties.

In this exercise, a number of relations are defined on the set \( A = \{0, 1, 2, 3\} \). For each relation, follow these instructions:

a. Draw the directed graph.

b. Determine whether the relation is reflexive.

c. Determine whether the relation is symmetric.

d. Determine whether the relation is transitive.

Provide a counterexample in each case in which the relation does not satisfy one of the properties.

8. \( R_8 = \{(0, 0), (1, 1)\} \)

This expression defines a relation \( R_8 \) on a set, consisting of two ordered pairs: (0, 0) and (1, 1). Each pair represents a relationship between two elements in the set. In educational contexts, such relationships are often explored in set theory and discrete mathematics to understand mappings and connections between elements.

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