1. MAT 3100 Introduction to Proof
04 Methods of Proof II

2. I cannot see some of the symbols!
Download the trial version of MATH TYPE equation edition from design science

3. Preview of More Reviews
Indirect Proofs
Contradiction
Proof by Contrapositive is considered as a special case of proof by contradiction
Proof by cases
Existence proofs

4. Proof by Contradiction
Proof by Contrapositive
Proof by Contradiction

5. Example 1
Analysis
Proof

6. Proof by Contradiction
Analysis
Proof by Contradiction of If-then Theorem
Suppose the negation of the conclusion is true.
Find a contradiction.
State the conclusion.

7. Proof by Contradiction
The method also work with statements other then If P then Q

8. Example 2
Analysis
Proof

9. Pause Here
Classwork

10. Proof by Cases

11. Example 3
Analysis
Proof

12. Proof by Cases Analysis Proof by Cases of If-then Theorem
Split the domain of interest into cases.
Prove each case separately.
State the conclusion.
Note that the cases do not have to be mutually exclusive. They just have to cover all elements in the domain.

13. Existence Proofs

14. Example 4
Analysis
Proof

15. Existence Proofs Analysis Existence Proof
Prove the statement by exhibiting an element in the domain of interest that satisfies the given conditions.
State the conclusion.

16. Group Explorations 04 Very fun to do.
Keep your voices down…you do not want to spoil the fun for the other groups.