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A Summary of Proofs and Proof Techniques

Most of the theorems and proofs in these notes are taken from Discrete Mathematics and Its Applications, by Rosen, with additional detail added.

  1. What is a proof?

  2. Why are proofs important?

  3. Equational proofs

  4. Mean what you write

  5. Substitution

  6. Substitution for specialization

  7. Forward proofs and the fact bank

  8. Using facts from the bank

  9. Proof by cases

  10. Proving ∀xP(x)

  11. Proving ∃xP(x)

  12. Proving A → B

  13. The importance of definitions

  14. Proving A ↔ B

  15. Proving ∀x∃yP(x,y)

  16. Proof by contradiction

  17. Backward proofs

  18. Proof by mathematical induction