For each of these pairs of sets in 1–3 determine whether the first is a subset of the second, the second is asubset of the first, or neither is a subset of the other.1. The set of airline flights from New York to New Delhi, the set of nonstop airline flights from New Yorkto New Delhi2. The set of people who speak English, the set of people who speak Chinese3. The set of flying squirrels, the set of living creatures that can fly4. Use a Venn diagram to illustrate the set of all months of the year whose names do not contain the letterR 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 illustratethe relationships A ⊂ B and B ⊂ C.6. Prove that A ∩ B = A ∪ B by giving an element table proof.7. Prove that A ∩ B = A ∪ B by giving a proof using logical equivalence.8. Prove that A ∩ B = A ∪ 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 bedirected 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 thereare four flights from Boston to Newark, two flights from Newark to Boston, three flights from Newark toMiami, two flights from Miami to Newark, one flight from Newark to Detroit, two flights from Detroit toNewark, three flights from Newark to Washington, two flights from Washington to Newark, and one flightfrom Washington to Miami, with an edge between vertices representing cities that have a flight betweenthem (in either direction). Question 1Draw graph models, stating the type of graph used, to representairline routes where every day there are four flights from Bostonto Newark, two flights from Newark to Boston, three flights fromNewark to Miami, two flights from Miami to Newark, one flightfrom Newark to Detroit, two flights from Detroit to Newark, threeflights from Newark to Washington, two flights from Washingtonto Newark, and one flight from Washington to Miami, with anedge from a vertex representing a city where a flight starts to thevertex representing the city where it ends.

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