Proofs by Counterexample

• Read carefully pages 120 through 124 (section 5.1)
• Some key questions to answer (try these without looking at the book, but after you’ve read the book):
  1. What do we call a “counterexample”?
  2. What statements does a counterexample approach allow us to prove?
  3. Can a counterexample be used to prove a statement \(\sim \exists x,\,P(x)\) is false?
  4. Give various examples of proof by counterexample.
• Practice problems from section 5.1 (page 137): 5.2, 5.3, 5.6, 5.9