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MAT422: Sept 2012 – Jan 2013

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Mathematical Logic & Proving Techniques

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Class Schedule

Monday

- 1400-1550 – MAT422 (CSB2At, CSB3At, CSB4At, CSB4Bt) A108-TEC

Wednesday

- 1600-1650 – MAT422 (CSB2At, CSB3At, CSB4At, CSB4Bt) A214
- 1700-1750 – MAT422 (CSB2At, CSB3At) A214

Thursday

- 1500-1550 – MAT422 (CSB4At, CSB4Bt) F232

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Contents

- Set Theory
- Sets and Subsets
- Set Operations
- Laws of Set Theory
- Counting and Venn Diagrams

- Logic
- Propositions: primitive, compound, truth values
- Logical connectives and truth tables; negation, conjunction, disjunction, implication, biconditional
- Converse, contrapositive, inverse
- Translating English statements into symbolic form
- Tautology, contradiction
- Logical equivalences
- Laws of logic, principle of duality
- Logical implication
- Arguments – validity of arguments by using truth tables and rules of inference, invalidity of arguments by using counterexamples
- Quantifiers – existential and universal quantifiers, logical
connectives and negations, logical equivalences, logical implications
- Nested Quantifiers

- How to do proofs
- Introduction
- The Forward – Backward method
- Definitions and Mathematical Terminology
- The Construction Method
- The Choose Method
- Specialization Method
- Negations
- The Contradiction Method
- The Contrapositive Method
- Induction Method

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Textbooks

- Douglas Ralph P. Grimaldi, Discrete and Combinatorial Mathematics, 4th edition, Addison Wesley, 1999.
- Daniel Solow, How to Read and Do Proofs, 4th edition. John Wiley & Sons, 2005.

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