MAT 3100 Introduction to Proof 04 Methods of

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MAT 3100 Introduction to Proof 04 Methods of Proof II http: //myhome. spu. edu/lauw

MAT 3100 Introduction to Proof 04 Methods of Proof II http: //myhome. spu. edu/lauw

I cannot see some of the symbols! l l Download the trial version of

I cannot see some of the symbols! l l Download the trial version of MATH TYPE equation edition from design science http: //www. dessci. com/en/products/math type/trial. asp

Preview of More Reviews l Indirect Proofs • Contradiction • Proof by Contrapositive is

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

Proof by Contradiction l Proof by Contrapositive l Proof by Contradiction

Proof by Contradiction l Proof by Contrapositive l Proof by Contradiction

Example 1 Analysis Proof

Example 1 Analysis Proof

Proof by Contradiction Analysis Proof by Contradiction of If-then Theorem • Suppose the negation

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.

Proof by Contradiction l The method also work with statements other then If P

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

Example 2 Analysis Proof

Example 2 Analysis Proof

Pause Here l Classwork

Pause Here l Classwork

Proof by Cases

Proof by Cases

Example 3 Analysis Proof

Example 3 Analysis Proof

Proof by Cases Analysis Proof by Cases of If-then Theorem • Split the domain

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.

Existence Proofs

Existence Proofs

Example 4 Analysis Proof

Example 4 Analysis Proof

Existence Proofs Analysis Existence Proof • Prove the statement by exhibiting an element in

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.

Group Explorations 04 l l Very fun to do. Keep your voices down…you do

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

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