HIT400 Discrete Structures Assignment 1: Graph Theory and Functions
VerifiedAdded on 2023/06/04
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Homework Assignment
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This assignment solution addresses three problems related to discrete structures. The first problem explores functions and their compositions, including the analysis of a function f: R → [0,1] and g: [0,1] → [-1,1], and the evaluation of (g o f)(x) and (f o g)(x). The second problem involves mathematical induction, specifically proving or disproving the inequality ∑(2i-1)/i^4 ≤ 4 - (2n+1)/n^2. The third problem delves into graph theory, examining a given graph's properties. The analysis includes determining if the graph is complete, regular, connected, Eulerian, or Hamiltonian, and identifying a spanning tree and demonstrating graph isomorphism between two graphs. The solution provides detailed explanations and justifications for each part of the problems.
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