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.
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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![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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13840a37-a087-408f-a8f1-6788fad34e23%2F1133ff57-76ad-4514-acad-e9b525a48aa3%2F1lmjgpj_processed.png&w=3840&q=75)
Transcribed Image Text: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.
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