Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 14 - Graph Theory - 14.1 Graphs, Paths, and Circuits - Exercise Set 14.1: 68

Answer

The original statement makes sense.

Work Step by Step

A path is a sequence of adjacent vertices in a graph. If a path starts and ends at the same vertex, then the path is a circuit. Thus, a circuit is a specific type of path. However, there are many paths which are not circuits. If a path starts at one vertex and ends at a different vertex, then the path is not a circuit. The original statement makes sense. The path along this graph is not a circuit. There are many paths which are not circuits, so it makes sense that there could be a path that is not a circuit.
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