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Exercise 22 (Chapter Review)

Avg difficulty 2.5

Consider the statement “If a graph is planar, then it has an Euler path.”

  1. Write the converse of the statement.

  2. Write the contrapositive of the statement.

  3. Write the negation of the statement.

  4. Is it possible for the contrapositive to be false? If it was, what would that tell you?

  5. Is the original statement true or false? Prove your answer.

  6. Is the converse of the statement true or false? Prove your answer.

Levin, Discrete Mathematics: An Open Introduction (3rd ed.), §5.7 Chapter Summary, Chapter Review, Exercise 22

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Adapted from Discrete Mathematics: An Open Introduction © 2013–2019 Oscar Levin. Licensed under CC BY-SA 4.0. Source: Discrete Mathematics: An Open Introduction. Imported at revision 1e2e26b.