Many approximation algorithms for the Traveling Salesman Problem (TSP) assume that the graph satisfies the triangle inequality : \[ c(x,y) \le c(x,z) + c(z,y) \] for any vertices \(x\), \(y\), and \(z\). This assumption is used in algorithms such as Rosenkrantz-Stearns-Lewis and Christofides . Problem Statement Which of the following statements is true? a) Consider a complete weighted graph whose vertices are points in \(\mathbb{R}^3\). The weight of an edge is the Euclidean distance between its endpoints. In this graph, the triangle inequality is guaranteed to hold. b) Consider a complete weighted graph whose vertices are points in \(\mathbb{R}^3\). The weight of an edge is the square of the Euclidean distance between its endpoints. In this graph, the triangle inequality is guaranteed to hold. c) Consider a complete weighted graph whose edge weights are chosen independently by a random process . In this grap...