A playground consists of several structures, some of which are connected by bridges. The ground is covered with bark chips. Define a relation on the set of structures on the playground as follows: two structures are related if it is possible for a child to get from one to the other without walking on the bark chips (otherwise known as "hot lava"). (a) Can you imagine a playground for which this would not be an equiv- alence relation? Explain. (b) Suppose this relation is an equivalence. In the language of play- ground equipment, describe the equivalence classes.

A playground consists of several structures, some of which are connected by bridges. The ground is covered with bark chips. Define a relation on the set of structures on the playground as follows: two structures are related if it is possible for a child to get from one to the other without walking on the bark chips (otherwise known as "hot lava"). (a) Can you imagine a playground for which this would not be an equiv- alence relation? Explain. (b) Suppose this relation is an equivalence. In the language of play- ground equipment, describe the equivalence classes.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.7: Relations

Problem 14E: In each of the following parts, a relation is defined on the set of all human beings. Determine...

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