Answered: For each of these pairs of sets in 1–3…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

For each of these pairs of sets in 1–3 determine whether the first is a subset of the second, the second is a subset 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 York to New Delhi 2. The set of people who speak English, the set of people who speak Chinese 3. The set of flying squirrels, the set of living creatures that can fly 4. 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 ⊂ 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 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).