CPSC 125 Ch 1 sec 1

Logic: The foundation of reasoning ,[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Logic: The foundation of reasoning ,[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Statement ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Statements and Logic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Statements and Logical Connectives ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Statements and Logical Connectives ,[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Definitions for Logical Connectives ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Definitions for Logical Connectives ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Another form of implication ,[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies A B A  B T T T T F F F T T F F T A A  B A  V B T F T T T F F F F T T T F T F T

Definitions for Logical Connectives ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies A B A  B B  A (A  B) Λ (B  A) T T T T T T F F T F F T T F F F F T T T

Definitions for Logical Connectives ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Truth Tables ,[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies A A  T F F T A B A Λ B T T T T F F F T F F F F A B A V B T T T T F T F T T F F F A B A  B T T T T F F F T T F F T A B A  B T T T T F F F T F F F T

Well Formed Formula (wff) ,[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Well Formed Formula (wff) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Truth Tables for some wffs ,[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies A B B  A V B  A V B (A V B)  A V B   (A V B)  T T F T T F F T F T T T F F F T F F T F T F F T T F T T

Wff with n statement letters ,[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Tautology and Contradiction ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Tautological Equivalences ,[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies A B C A V B B V C (A V B) V C A V (B V C) T T T T T T T T T F T T T T T F T T T T T T F F T F T T F T T T T T T F T F T T T T F F T F T T T F F F F F F F

Some Common Equivalences ,[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies Commutative A V B  B V A A Λ B  B Λ A Associative (A V B) V C  A V (B V C) (A Λ B) Λ C  A Λ (B Λ C) Distributive A V (B Λ C)  (A V B) Λ (A V C) A Λ (B V C)  (A Λ B) V (A Λ C) Identity A V 0  A A Λ 1  A Complement A V A   1 A Λ A   0

De Morgan’s Laws ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies A B A  B  A V B (A V B)  A  Λ B  T T F F T F F T F F T T F F F T T F T F F F F T T F T T

Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Pseudocode example ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

Tautology Test Algorithm ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Section 1.1 Statements, Symbolic Representations and Tautologies

CPSC 125 Ch 1 sec 1

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CPSC 125 Ch 1 sec 1

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