Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letter R in the set of all months of the year. 5. Use a Venn diagram to illustrate the relationship A ≤ B and B ≤ C. 15. Use a Venn diagram to illustrate the relationships A c B and B c C. 6. Prove that AB = Au B by giving an element table proof. 7. Prove that A B = A u B by giving a proof using logical equivalence. 8. Prove that An B = Au B by giving a Venn diagram proof. 9. Explain how graphs can be used to model the spread of a contagious disease. Should the edges be directed or undirected? Should multiple edges be allowed? Should loops be allowed? 10. Draw graph models, stating the type of graph used, to represent airline routes where every day there are four flights from Boston to Newark, two flights from Newark to Boston, three flights from Newark to Miami, two flights from Miami to Newark, one flight from Newark to Detroit, two flights from Detroit to Newark, three flights from Newark to Washington, two flights from Washington to Newark, and one flight from Washington to Miami, with an edge between vertices representing cities that have a flight between them (in either direction).