question on discrete math for computer science

-explanation is needed for every question

-graph are always assumed to be simple

Fully explain your answers for all questions. Throughout the assignment, graphs are always assumed to be simple. Q1. Eight students Alice, Bob, Casey, Drew, Eva, Francis, Glen, Hunter entered Monash University this year. Alice, Bob and Casey are from Canberra and Drew, Eva, Francis are from Newcastle. Glen and Hunter are international students from different countries. Alice, Casey and Hunter play tennis, while Drew, Francis, Glen and Hunter play soccer. Any two students from the same city or playing the same sport know each other. [2] (a) Draw a graph corresponding to the student acquaintances. Find its number of edges. (b) Write down the adjacency matrix for this graph. (c) Show that deleting any one of edges does not disconnect the graph. In the language of [3] Lecture 31 this is the same as saying the graph has no bridges. (d) Is it possible to seat all eight students at a round table in such a way that any of them [3] knows both neighbours. Justify your