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Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter...

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Slides for CISC 2315: Discrete Structures Chapters 6 & 7 CISC 2315 Discrete Structures Professor William G. Tanner, Jr. Fall 2008 Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.
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Page 1: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Slides for CISC 2315: Discrete Structures

Chapters 6 & 7

CISC 2315 Discrete Structures

Professor William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 2: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Chapter 6

Section 6.1 How does one reason?

CISC 2315 Discrete Structures

William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 3: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.1 How does one reason?

Page 4: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Chapter 6

Section 6.2 Propositional Calculus

CISC 2315 Discrete Structures

William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 5: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.2 Propositional Calculus

Page 6: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.2 Propositional Calculus

Page 7: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.2 Propositional Calculus

Page 8: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.2 Propositional Calculus

Page 9: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.2 Propositional Calculus

Page 10: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.2 Propositional Calculus

Page 11: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.2 Propositional Calculus

Page 12: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Chapter 6

Section 6.3 Formal Reasoning

CISC 2315 Discrete Structures

William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 13: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 14: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 15: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 16: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 17: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 18: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 19: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 20: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 21: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.3 Formal Reasoning

Page 22: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Chapter 6

Section 6.4 Formal Axiom Systems

CISC 2315 Discrete Structures

William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 23: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.4 Formal Axiom Systems

Page 24: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 6.4 Formal Axiom Systems

Page 25: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Chapter 7

Section 7.1 First-Order Predicate Calculus

CISC 2315 Discrete Structures

William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 26: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 27: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 28: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 29: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 30: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 31: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 32: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 33: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.1 First-Order Predicate Calculus

Page 34: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Chapter 7

Section 7.2 Equivalent Formulas

CISC 2315 Discrete Structures

William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 35: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.2 Equivalent Formulas

Page 36: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.2 Equivalent Formulas

Page 37: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.2 Equivalent Formulas

Page 38: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.2 Equivalent Formulas

Page 39: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.2 Equivalent Formulas

Page 40: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.2 Equivalent Formulas

Page 41: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.2 Equivalent Formulas

Page 42: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Chapter 7

Section 7.3 Formal Proofs in Predicate Calculus

CISC 2315 Discrete Structures

William G. Tanner, Jr.

Fall 2008

Slides created by James L. Hein, author of Discrete Structures, Logic, and Computability, 2002, 2nd Edition, Jones & Bartlett Computer Science, ISBN 0-7637-1843-2.

Page 43: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus

Page 44: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus

Page 45: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus

Page 46: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus

Page 47: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus

Page 48: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus

Page 49: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus

Page 50: Slides for CISC 2315: Discrete Structures Chapters 6 & 7mars.umhb.edu/~wgt/cisc2315/Chapter 6-7.pdfChapter 7 Section 7.1 First-Order Predicate Calculus CISC 2315 Discrete Structures

Section 7.3 Formal Proofs in Predicate Calculus


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