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If G contains a trail from x to y, then G contains a path from x to y.

a) True

b) False

1 Answer

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The given statement "If G contains a trail from x to y, then G contains a path from x to y" is true.

The statement is true because a trail is a sequence of edges in a graph where no edge (or vertex) is repeated. If a graph G contains a trail from vertex x to vertex y, it implies that there exists a sequence of edges that connects x to y without revisiting any edge. Since a path is a more general concept that allows for repeated vertices but not repeated edges, any trail can be considered a path.

Therefore, if G contains a trail from x to y, it also contains a path from x to y. In graph theory, a trail is a specific type of path, and the presence of a trail ensures the existence of a more general path between the specified vertices in the graph. Hence the given statement is true.

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