Exercise 22.

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.

Solution.
in-context