(Solution) - What is wrong with the following proof using mathematical induction -(2025 Original AI-Free Solution)

Discipline:

Type of Paper:

Academic Level: Undergrad. (yrs 3-4)

Paper Format: APA

Pages: 5 Words: 1375

Download Solution ($11.00) Write My Paper Afresh

Buy For $11.00

Paper Details

What is wrong with the following "proof" using mathematical induction of the statement that every tree with n vertices has a path of length n ? 1. Basis step: Every tree with one vertex clearly has a path of length 0. Inductive step: Assume that a tree with n vertices has a path of length n ? 1, which has u as its terminal vertex. Add a vertex v and the edge from u to v. The resulting tree has n + 1 vertices and has a path of length n. This completes the inductive step.