SlideShare a Scribd company logo

Truth Table Analysis

•Download as PPT, PDF•
•
Janet Stemwedel
Janet Stemwedel
Education
1 of 95
Indirect-Table Analysis Phil 57 section 3 San Jose State University Fall 2010
What are truth-tables good for? ,[object Object],[object Object],[object Object]
Sometimes we don’t need a full truth-table! ,[object Object],[object Object],[object Object],[object Object]
Example: P  Q, Q / P
Example: P  Q, Q / P Pr1 Pr2 C P Q P  Q Q P
Example: P  Q, Q / P ,[object Object],Pr1 Pr2 C P Q P  Q Q P
Example: P  Q, Q / P ,[object Object],Pr1 Pr2 C P Q P  Q Q P F F
Example: P  Q, Q / P ,[object Object],[object Object],Pr1 Pr2 C P Q P  Q Q P F F
Example: P  Q, Q / P ,[object Object],[object Object],Pr1 Pr2 C P Q P  Q Q P F T T F
Example: P  Q, Q / P ,[object Object],[object Object],Pr1 Pr2 C P Q P  Q Q P F T T T F
Example: P  Q, Q / P ,[object Object],[object Object],[object Object],Pr1 Pr2 C P Q P  Q Q P F T T T F
Detailed strategy:
Detailed strategy: ,[object Object]
Detailed strategy: ,[object Object],[object Object]
Detailed strategy: ,[object Object],[object Object],[object Object]
Detailed strategy: ,[object Object],[object Object],[object Object],[object Object]
Example 2: P  Q, P / Q ,[object Object]
Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q
Example 2: P  Q, P / Q ,[object Object],Pr1 Pr2 C P  Q P Q
Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q F
Example 2: P  Q, P / Q ,[object Object],Pr1 Pr2 C P  Q P Q F
Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T F
Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T T F
Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T F T F
Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T F T F F
Example 2: P  Q, P / Q ,[object Object],Pr1 Pr2 C P  Q P Q T F T F F
Example 2: P  Q, P / Q ,[object Object],[object Object],Pr1 Pr2 C P  Q P Q T F T F F
Example 3: P  Q, (R  Q)  S / P
Example 3: P  Q, (R  Q)  S / P ,[object Object]
Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P
Example 3: P  Q, (R  Q)  S / P ,[object Object],Pr1 Pr2 C P  Q (R  Q)  S P
Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F
Example 3: P  Q, (R  Q)  S / P ,[object Object],Pr1 Pr2 C P  Q (R  Q)  S P F
Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F F
Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F F T
Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F T F T
Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F T F T T
Example 3: P  Q, (R  Q)  S / P ,[object Object],Pr1 Pr2 C P  Q (R  Q)  S P F T F T T
Example 3: P  Q, (R  Q)  S / P ,[object Object],[object Object],Pr1 Pr2 C P  Q (R  Q)  S P F T F T T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object]
Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P
Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F
Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F
Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F
Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F F
Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F F F T T F F T T T F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F F F F T T F F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F F F F T T F F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F F F F T T T F F T T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T T F F F F F T T T F F T T T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F T F F F F F T T T F F T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F T T F T F F F F F T F F T T T T F F T T T T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F T F F F F F T T T F F T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T T F T F F F F F T T T T F F T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T T F T F F F F F T T T T F F T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],[object Object],[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T T F T F F F F F T T T T F F T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F T F T F F F F F T F T T T F F T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F T F T F F F F F T F F T T T F F T T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F T T F T F F F F F T F F T T T T F F T T T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F T T F T F F F F F T F F T T T T F F T T T T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F T T F T F F F F F T F F T T T T F F T T T T T T T F T F F F T
Example 4: P  Q, Q  R, ~S  V / V  P ,[object Object],[object Object],Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F T F F T T F T F F F F F T F F T T T T F F T T T T T T T F T F F F T
Indirect-tables to determine if a set of formulae is satisfiable:
Indirect-tables to determine if a set of formulae is satisfiable: ,[object Object]
Indirect-tables to determine if a set of formulae is satisfiable: ,[object Object],[object Object]
Indirect-tables to determine if a set of formulae is satisfiable: ,[object Object],[object Object],[object Object]
Example: P  Q, ~P  Q P  Q ~P  Q
Example: P  Q, ~P  Q P  Q ~P  Q T T
Example: P  Q, ~P  Q P  Q ~P  Q T T F F T F
Example: P  Q, ~P  Q Satisfiable P  Q ~P  Q T T F F T F
Example: P  Q, P  ~Q P  Q P  ~Q
Example: P  Q, P  ~Q P  Q P  ~Q T T
Example: P  Q, P  ~Q P  Q P  ~Q T T T T F
Example: P  Q, P  ~Q P  Q P  ~Q T T T F T T F
Example: P  Q, P  ~Q P  Q P  ~Q T T T F T T F F
Example: P  Q, P  ~Q Unsatisfiable P  Q P  ~Q T T T F T T F F
Example: P  ~Q, P  Q P  ~Q P  Q T T T F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T T T T T F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F T T T T F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T F F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T F F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T F F T F
Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T T F F T F
Example: P  ~Q, P  Q Satisfiable P  ~Q P  Q T F F T T T T T T T F F T F F T T F F T F
Summary of indirect-table tests: Test Procedure Results Satisfiability Place T under the main connective of each formula If there is at least one row where every formula can be T, the set is satisfiable. Validity Place T under every premise, F under conclusion If there is a row where premises are true and conclusion is false, argument is invalid.
Next time: Quiz #3 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Recommended

Truth table analysis
Truth table analysisTruth table analysis
Truth table analysisJanet Stemwedel
 
LOGIC
LOGICLOGIC
LOGICshahzadebaujiti
 
3 computing truth tables
3 computing truth tables3 computing truth tables
3 computing truth tablesjennytuazon01630
 
Truth tables
Truth tablesTruth tables
Truth tableswalkerlj
 
Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction,
Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction, Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction,
Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction, Ria Micor
 
Truth table a.r
Truth table a.rTruth table a.r
Truth table a.rSyed Umair
 
Exercise 1
Exercise 1Exercise 1
Exercise 1Amr Nady
 
Logic - Logical Propositions
Logic - Logical Propositions Logic - Logical Propositions
Logic - Logical Propositions JosefMikaeldelCorro
 

Recommended

Truth table analysis
Truth table analysisTruth table analysis
Truth table analysisJanet Stemwedel
 
LOGIC
LOGICLOGIC
LOGICshahzadebaujiti
 
3 computing truth tables
3 computing truth tables3 computing truth tables
3 computing truth tablesjennytuazon01630
 
Truth tables
Truth tablesTruth tables
Truth tableswalkerlj
 
Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction,
Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction, Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction,
Logic (LESSON) - Truth Table, Negation, Conjunction, Dis junction, Ria Micor
 
Truth table a.r
Truth table a.rTruth table a.r
Truth table a.rSyed Umair
 
Exercise 1
Exercise 1Exercise 1
Exercise 1Amr Nady
 
Logic - Logical Propositions
Logic - Logical Propositions Logic - Logical Propositions
Logic - Logical Propositions JosefMikaeldelCorro
 
Formal Logic - Lesson 3 - Truth Tables
Formal Logic - Lesson 3 - Truth TablesFormal Logic - Lesson 3 - Truth Tables
Formal Logic - Lesson 3 - Truth TablesLaguna State Polytechnic University
 
Mathematical foundations of computer science
Mathematical foundations of computer scienceMathematical foundations of computer science
Mathematical foundations of computer scienceBindhuBhargaviTalasi
 
Logic&proof
Logic&proofLogic&proof
Logic&proofFathan Hakim
 
Logic and proof
Logic and proofLogic and proof
Logic and proofSuresh Ram
 
Assignement of discrete mathematics
Assignement of discrete mathematicsAssignement of discrete mathematics
Assignement of discrete mathematicsSyed Umair
 
Truth, deduction, computation lecture 6
Truth, deduction, computation lecture 6Truth, deduction, computation lecture 6
Truth, deduction, computation lecture 6Vlad Patryshev
 
Propositional logic
Propositional logicPropositional logic
Propositional logicForwardBlog Enewzletter
 
Dm assignment2
Dm assignment2Dm assignment2
Dm assignment2H K
 
Propositional logic by shawan
Propositional logic by shawanPropositional logic by shawan
Propositional logic by shawanTouhidul Shawan
 
Propositional Logic (Descreate Mathematics)
Propositional Logic (Descreate Mathematics)Propositional Logic (Descreate Mathematics)
Propositional Logic (Descreate Mathematics)Abdullah Al Amin
 
Mathematical Logic
Mathematical LogicMathematical Logic
Mathematical LogicSepti Ratnasari
 
Solution2
Solution2Solution2
Solution2H K
 
Translating English to Propositional Logic
Translating English to Propositional LogicTranslating English to Propositional Logic
Translating English to Propositional LogicJanet Stemwedel
 
Chapter 1 Logic of Compound Statements
Chapter 1 Logic of Compound StatementsChapter 1 Logic of Compound Statements
Chapter 1 Logic of Compound Statementsguestd166eb5
 
Logic (PROPOSITIONS)
Logic (PROPOSITIONS)Logic (PROPOSITIONS)
Logic (PROPOSITIONS)D Nayanathara
 
Logic worksheet
Logic worksheetLogic worksheet
Logic worksheetAlejandroBuhia
 
Formal Logic - Lesson 4 - Tautology, Contradiction and Contingency
Formal Logic - Lesson 4 - Tautology, Contradiction and ContingencyFormal Logic - Lesson 4 - Tautology, Contradiction and Contingency
Formal Logic - Lesson 4 - Tautology, Contradiction and ContingencyLaguna State Polytechnic University
 
Logic (slides)
Logic (slides)Logic (slides)
Logic (slides)IIUM
 
Climategate and scientific methodology
Climategate and scientific methodologyClimategate and scientific methodology
Climategate and scientific methodologyJanet Stemwedel
 
Feminist Critiques of Science
Feminist Critiques of ScienceFeminist Critiques of Science
Feminist Critiques of ScienceJanet Stemwedel
 
P160 Duhem and Quine
P160 Duhem and QuineP160 Duhem and Quine
P160 Duhem and QuineJanet Stemwedel
 
Lec15 Patents and Intellectual Property
Lec15 Patents and Intellectual PropertyLec15 Patents and Intellectual Property
Lec15 Patents and Intellectual PropertyJanet Stemwedel
 

More Related Content

What's hot

Mathematical foundations of computer science
Mathematical foundations of computer scienceMathematical foundations of computer science
Mathematical foundations of computer scienceBindhuBhargaviTalasi
 
Logic and proof
Logic and proofLogic and proof
Logic and proofSuresh Ram
 
Assignement of discrete mathematics
Assignement of discrete mathematicsAssignement of discrete mathematics
Assignement of discrete mathematicsSyed Umair
 
Truth, deduction, computation lecture 6
Truth, deduction, computation lecture 6Truth, deduction, computation lecture 6
Truth, deduction, computation lecture 6Vlad Patryshev
 
Dm assignment2
Dm assignment2Dm assignment2
Dm assignment2H K
 
Propositional logic by shawan
Propositional logic by shawanPropositional logic by shawan
Propositional logic by shawanTouhidul Shawan
 
Propositional Logic (Descreate Mathematics)
Propositional Logic (Descreate Mathematics)Propositional Logic (Descreate Mathematics)
Propositional Logic (Descreate Mathematics)Abdullah Al Amin
 
Solution2
Solution2Solution2
Solution2H K
 
Translating English to Propositional Logic
Translating English to Propositional LogicTranslating English to Propositional Logic
Translating English to Propositional LogicJanet Stemwedel
 
Chapter 1 Logic of Compound Statements
Chapter 1 Logic of Compound StatementsChapter 1 Logic of Compound Statements
Chapter 1 Logic of Compound Statementsguestd166eb5
 
Logic (PROPOSITIONS)
Logic (PROPOSITIONS)Logic (PROPOSITIONS)
Logic (PROPOSITIONS)D Nayanathara
 
Formal Logic - Lesson 4 - Tautology, Contradiction and Contingency
Formal Logic - Lesson 4 - Tautology, Contradiction and ContingencyFormal Logic - Lesson 4 - Tautology, Contradiction and Contingency
Formal Logic - Lesson 4 - Tautology, Contradiction and ContingencyLaguna State Polytechnic University
 
Logic (slides)
Logic (slides)Logic (slides)
Logic (slides)IIUM
 

What's hot (18)

Formal Logic - Lesson 3 - Truth Tables
Formal Logic - Lesson 3 - Truth TablesFormal Logic - Lesson 3 - Truth Tables
Formal Logic - Lesson 3 - Truth Tables
 
Mathematical foundations of computer science
Mathematical foundations of computer scienceMathematical foundations of computer science
Mathematical foundations of computer science
 
Logic&proof
Logic&proofLogic&proof
Logic&proof
 
Logic and proof
Logic and proofLogic and proof
Logic and proof
 
Assignement of discrete mathematics
Assignement of discrete mathematicsAssignement of discrete mathematics
Assignement of discrete mathematics
 
Truth, deduction, computation lecture 6
Truth, deduction, computation lecture 6Truth, deduction, computation lecture 6
Truth, deduction, computation lecture 6
 
Propositional logic
Propositional logicPropositional logic
Propositional logic
 
Dm assignment2
Dm assignment2Dm assignment2
Dm assignment2
 
Propositional logic by shawan
Propositional logic by shawanPropositional logic by shawan
Propositional logic by shawan
 
Propositional Logic (Descreate Mathematics)
Propositional Logic (Descreate Mathematics)Propositional Logic (Descreate Mathematics)
Propositional Logic (Descreate Mathematics)
 
Mathematical Logic
Mathematical LogicMathematical Logic
Mathematical Logic
 
Solution2
Solution2Solution2
Solution2
 
Translating English to Propositional Logic
Translating English to Propositional LogicTranslating English to Propositional Logic
Translating English to Propositional Logic
 
Chapter 1 Logic of Compound Statements
Chapter 1 Logic of Compound StatementsChapter 1 Logic of Compound Statements
Chapter 1 Logic of Compound Statements
 
Logic (PROPOSITIONS)
Logic (PROPOSITIONS)Logic (PROPOSITIONS)
Logic (PROPOSITIONS)
 
Logic worksheet
Logic worksheetLogic worksheet
Logic worksheet
 
Formal Logic - Lesson 4 - Tautology, Contradiction and Contingency
Formal Logic - Lesson 4 - Tautology, Contradiction and ContingencyFormal Logic - Lesson 4 - Tautology, Contradiction and Contingency
Formal Logic - Lesson 4 - Tautology, Contradiction and Contingency
 
Logic (slides)
Logic (slides)Logic (slides)
Logic (slides)
 

Viewers also liked

Climategate and scientific methodology
Climategate and scientific methodologyClimategate and scientific methodology
Climategate and scientific methodologyJanet Stemwedel
 
Feminist Critiques of Science
Feminist Critiques of ScienceFeminist Critiques of Science
Feminist Critiques of ScienceJanet Stemwedel
 
Lec15 Patents and Intellectual Property
Lec15 Patents and Intellectual PropertyLec15 Patents and Intellectual Property
Lec15 Patents and Intellectual PropertyJanet Stemwedel
 
P160 antirealismclassroomversion
P160 antirealismclassroomversionP160 antirealismclassroomversion
P160 antirealismclassroomversionJanet Stemwedel
 
Explanation classroomversion
Explanation classroomversionExplanation classroomversion
Explanation classroomversionJanet Stemwedel
 
P160 Kuhn and his Critics
P160 Kuhn and his CriticsP160 Kuhn and his Critics
P160 Kuhn and his CriticsJanet Stemwedel
 

Viewers also liked (8)

Climategate and scientific methodology
Climategate and scientific methodologyClimategate and scientific methodology
Climategate and scientific methodology
 
Feminist Critiques of Science
Feminist Critiques of ScienceFeminist Critiques of Science
Feminist Critiques of Science
 
P160 Duhem and Quine
P160 Duhem and QuineP160 Duhem and Quine
P160 Duhem and Quine
 
Lec15 Patents and Intellectual Property
Lec15 Patents and Intellectual PropertyLec15 Patents and Intellectual Property
Lec15 Patents and Intellectual Property
 
P160 antirealismclassroomversion
P160 antirealismclassroomversionP160 antirealismclassroomversion
P160 antirealismclassroomversion
 
P160 hempelhume
P160 hempelhumeP160 hempelhume
P160 hempelhume
 
Explanation classroomversion
Explanation classroomversionExplanation classroomversion
Explanation classroomversion
 
P160 Kuhn and his Critics
P160 Kuhn and his CriticsP160 Kuhn and his Critics
P160 Kuhn and his Critics
 

Similar to Truth Table Analysis

Nature of Logic.pptx
Nature of Logic.pptxNature of Logic.pptx
Nature of Logic.pptxMath101BSCA1C
 
Discreate Truth tables and laws of logic
Discreate Truth tables and laws of logicDiscreate Truth tables and laws of logic
Discreate Truth tables and laws of logicZenLooper
 
Assignement of discrete mathematics
Assignement of discrete mathematicsAssignement of discrete mathematics
Assignement of discrete mathematicsSyed Umair
 
Maths teachers guide For freshman course.pdf
Maths teachers guide For freshman course.pdfMaths teachers guide For freshman course.pdf
Maths teachers guide For freshman course.pdfhabtamu292245
 
Ontology model and owl
Ontology model and owlOntology model and owl
Ontology model and owlStanley Wang
 
Lecture-3-and-4.pdf
Lecture-3-and-4.pdfLecture-3-and-4.pdf
Lecture-3-and-4.pdfssuserc478ac
 
UNIT-III-PPT.pptx
UNIT-III-PPT.pptxUNIT-III-PPT.pptx
UNIT-III-PPT.pptxDakshBaveja
 

Similar to Truth Table Analysis (9)

null-12.pdf
null-12.pdfnull-12.pdf
null-12.pdf
 
null-12.pdf
null-12.pdfnull-12.pdf
null-12.pdf
 
Nature of Logic.pptx
Nature of Logic.pptxNature of Logic.pptx
Nature of Logic.pptx
 
Discreate Truth tables and laws of logic
Discreate Truth tables and laws of logicDiscreate Truth tables and laws of logic
Discreate Truth tables and laws of logic
 
Assignement of discrete mathematics
Assignement of discrete mathematicsAssignement of discrete mathematics
Assignement of discrete mathematics
 
Maths teachers guide For freshman course.pdf
Maths teachers guide For freshman course.pdfMaths teachers guide For freshman course.pdf
Maths teachers guide For freshman course.pdf
 
Ontology model and owl
Ontology model and owlOntology model and owl
Ontology model and owl
 
Lecture-3-and-4.pdf
Lecture-3-and-4.pdfLecture-3-and-4.pdf
Lecture-3-and-4.pdf
 
UNIT-III-PPT.pptx
UNIT-III-PPT.pptxUNIT-III-PPT.pptx
UNIT-III-PPT.pptx
 

More from Janet Stemwedel

P160 Hempel, Hume, Deduction, and Induction
P160 Hempel, Hume, Deduction, and InductionP160 Hempel, Hume, Deduction, and Induction
P160 Hempel, Hume, Deduction, and InductionJanet Stemwedel
 
Lect10 Human Subjects: History
Lect10 Human Subjects: HistoryLect10 Human Subjects: History
Lect10 Human Subjects: HistoryJanet Stemwedel
 
Lect11 Human Subjects: Regulations
Lect11 Human Subjects: RegulationsLect11 Human Subjects: Regulations
Lect11 Human Subjects: RegulationsJanet Stemwedel
 
Lec12 Human Subjects:Global Issues
Lec12 Human Subjects:Global IssuesLec12 Human Subjects:Global Issues
Lec12 Human Subjects:Global IssuesJanet Stemwedel
 
Lec13 Scientific Papers and Communications
Lec13 Scientific Papers and CommunicationsLec13 Scientific Papers and Communications
Lec13 Scientific Papers and CommunicationsJanet Stemwedel
 
Lec 14 Authorship Issues
Lec 14 Authorship IssuesLec 14 Authorship Issues
Lec 14 Authorship IssuesJanet Stemwedel
 
Lec16 International Strategies for Scientific Dialogue
Lec16 International Strategies for Scientific DialogueLec16 International Strategies for Scientific Dialogue
Lec16 International Strategies for Scientific DialogueJanet Stemwedel
 
P160 naturalismclassroomlect
P160 naturalismclassroomlectP160 naturalismclassroomlect
P160 naturalismclassroomlectJanet Stemwedel
 
P160 Kuhn classroom Lecture 2
P160 Kuhn classroom Lecture 2P160 Kuhn classroom Lecture 2
P160 Kuhn classroom Lecture 2Janet Stemwedel
 
Kuhn: Paradigms and Normal Science
Kuhn: Paradigms and Normal ScienceKuhn: Paradigms and Normal Science
Kuhn: Paradigms and Normal ScienceJanet Stemwedel
 
Syntax and semantics of propositional logic
Syntax and semantics of propositional logicSyntax and semantics of propositional logic
Syntax and semantics of propositional logicJanet Stemwedel
 
Deductive and Inductive Arguments
Deductive and Inductive ArgumentsDeductive and Inductive Arguments
Deductive and Inductive ArgumentsJanet Stemwedel
 
Arguments (and other things)
Arguments (and other things)Arguments (and other things)
Arguments (and other things)Janet Stemwedel
 
Patents and intellectual property
Patents and intellectual propertyPatents and intellectual property
Patents and intellectual propertyJanet Stemwedel
 
Scientific Papers and Communications
Scientific Papers and CommunicationsScientific Papers and Communications
Scientific Papers and CommunicationsJanet Stemwedel
 

More from Janet Stemwedel (20)

P160 Hempel, Hume, Deduction, and Induction
P160 Hempel, Hume, Deduction, and InductionP160 Hempel, Hume, Deduction, and Induction
P160 Hempel, Hume, Deduction, and Induction
 
Lect10 Human Subjects: History
Lect10 Human Subjects: HistoryLect10 Human Subjects: History
Lect10 Human Subjects: History
 
Lect11 Human Subjects: Regulations
Lect11 Human Subjects: RegulationsLect11 Human Subjects: Regulations
Lect11 Human Subjects: Regulations
 
Lec12 Human Subjects:Global Issues
Lec12 Human Subjects:Global IssuesLec12 Human Subjects:Global Issues
Lec12 Human Subjects:Global Issues
 
Lec13 Scientific Papers and Communications
Lec13 Scientific Papers and CommunicationsLec13 Scientific Papers and Communications
Lec13 Scientific Papers and Communications
 
Lec 14 Authorship Issues
Lec 14 Authorship IssuesLec 14 Authorship Issues
Lec 14 Authorship Issues
 
Lec16 International Strategies for Scientific Dialogue
Lec16 International Strategies for Scientific DialogueLec16 International Strategies for Scientific Dialogue
Lec16 International Strategies for Scientific Dialogue
 
P160 naturalismclassroomlect
P160 naturalismclassroomlectP160 naturalismclassroomlect
P160 naturalismclassroomlect
 
P160 Kuhn classroom Lecture 2
P160 Kuhn classroom Lecture 2P160 Kuhn classroom Lecture 2
P160 Kuhn classroom Lecture 2
 
Propositional logic
Propositional logicPropositional logic
Propositional logic
 
Kuhn: Paradigms and Normal Science
Kuhn: Paradigms and Normal ScienceKuhn: Paradigms and Normal Science
Kuhn: Paradigms and Normal Science
 
Syntax and semantics of propositional logic
Syntax and semantics of propositional logicSyntax and semantics of propositional logic
Syntax and semantics of propositional logic
 
Quiz1 postmortem
Quiz1 postmortemQuiz1 postmortem
Quiz1 postmortem
 
Deductive and Inductive Arguments
Deductive and Inductive ArgumentsDeductive and Inductive Arguments
Deductive and Inductive Arguments
 
Language of Arguments
Language of ArgumentsLanguage of Arguments
Language of Arguments
 
Diagramming arguments
Diagramming argumentsDiagramming arguments
Diagramming arguments
 
Arguments (and other things)
Arguments (and other things)Arguments (and other things)
Arguments (and other things)
 
Patents and intellectual property
Patents and intellectual propertyPatents and intellectual property
Patents and intellectual property
 
Authorship Issues
Authorship IssuesAuthorship Issues
Authorship Issues
 
Scientific Papers and Communications
Scientific Papers and CommunicationsScientific Papers and Communications
Scientific Papers and Communications
 

Recently uploaded

Alper Gobel In Media Res Media Component
Alper Gobel In Media Res Media ComponentAlper Gobel In Media Res Media Component
Alper Gobel In Media Res Media ComponentInMediaRes1
 
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdfssuser54595a
 
MENTAL STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docxMENTAL STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docxPoojaSen20
 
APM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAPM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAssociation for Project Management
 
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptxContemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptxRoyAbrique
 
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityParis 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityGeoBlogs
 
Presiding Officer Training module 2024 lok sabha elections
Presiding Officer Training module 2024 lok sabha electionsPresiding Officer Training module 2024 lok sabha elections
Presiding Officer Training module 2024 lok sabha electionsanshu789521
 
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17Celine George
 
Science 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its CharacteristicsScience 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its CharacteristicsKarinaGenton
 
Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology ( Production , Purification , and Application ) Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology ( Production , Purification , and Application ) Sakshi Ghasle
 
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxHow to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxmanuelaromero2013
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Educationpboyjonauth
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxheathfieldcps1
 
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptxPOINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptxSayali Powar
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)eniolaolutunde
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactdawncurless
 
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Krashi Coaching
 

Recently uploaded (20)

Alper Gobel In Media Res Media Component
Alper Gobel In Media Res Media ComponentAlper Gobel In Media Res Media Component
Alper Gobel In Media Res Media Component
 
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
18-04-UA_REPORT_MEDIALITERAСY_INDEX-DM_23-1-final-eng.pdf
 
MENTAL STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docxMENTAL STATUS EXAMINATION format.docx
MENTAL STATUS EXAMINATION format.docx
 
APM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across SectorsAPM Welcome, APM North West Network Conference, Synergies Across Sectors
APM Welcome, APM North West Network Conference, Synergies Across Sectors
 
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptxContemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
Contemporary philippine arts from the regions_PPT_Module_12 [Autosaved] (1).pptx
 
Paris 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activityParis 2024 Olympic Geographies - an activity
Paris 2024 Olympic Geographies - an activity
 
Presiding Officer Training module 2024 lok sabha elections
Presiding Officer Training module 2024 lok sabha electionsPresiding Officer Training module 2024 lok sabha elections
Presiding Officer Training module 2024 lok sabha elections
 
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
Incoming and Outgoing Shipments in 1 STEP Using Odoo 17
 
Science 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its CharacteristicsScience 7 - LAND and SEA BREEZE and its Characteristics
Science 7 - LAND and SEA BREEZE and its Characteristics
 
Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology ( Production , Purification , and Application ) Hybridoma Technology ( Production , Purification , and Application )
Hybridoma Technology ( Production , Purification , and Application )
 
Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝
Model Call Girl in Tilak Nagar Delhi reach out to us at 🔝9953056974🔝
 
How to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptxHow to Make a Pirate ship Primary Education.pptx
How to Make a Pirate ship Primary Education.pptx
 
Introduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher EducationIntroduction to ArtificiaI Intelligence in Higher Education
Introduction to ArtificiaI Intelligence in Higher Education
 
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdfTataKelola dan KamSiber Kecerdasan Buatan v022.pdf
TataKelola dan KamSiber Kecerdasan Buatan v022.pdf
 
Staff of Color (SOC) Retention Efforts DDSD
Staff of Color (SOC) Retention Efforts DDSDStaff of Color (SOC) Retention Efforts DDSD
Staff of Color (SOC) Retention Efforts DDSD
 
The basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptxThe basics of sentences session 2pptx copy.pptx
The basics of sentences session 2pptx copy.pptx
 
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptxPOINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
POINT- BIOCHEMISTRY SEM 2 ENZYMES UNIT 5.pptx
 
Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)Software Engineering Methodologies (overview)
Software Engineering Methodologies (overview)
 
Accessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impactAccessible design: Minimum effort, maximum impact
Accessible design: Minimum effort, maximum impact
 
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
Kisan Call Centre - To harness potential of ICT in Agriculture by answer farm...
 

Truth Table Analysis

  • 1. Indirect-Table Analysis Phil 57 section 3 San Jose State University Fall 2010
  • 2.
  • 3.
  • 4. Example: P  Q, Q / P
  • 5. Example: P  Q, Q / P Pr1 Pr2 C P Q P  Q Q P
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 13.
  • 14.
  • 15.
  • 16.
  • 17.
  • 18. Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q
  • 19.
  • 20. Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q F
  • 21.
  • 22. Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T F
  • 23. Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T T F
  • 24. Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T F T F
  • 25. Example 2: P  Q, P / Q Pr1 Pr2 C P  Q P Q T F T F F
  • 26.
  • 27.
  • 28. Example 3: P  Q, (R  Q)  S / P
  • 29.
  • 30. Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P
  • 31.
  • 32. Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F
  • 33.
  • 34. Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F F
  • 35. Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F F T
  • 36. Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F T F T
  • 37. Example 3: P  Q, (R  Q)  S / P Pr1 Pr2 C P  Q (R  Q)  S P F T F T T
  • 38.
  • 39.
  • 40.
  • 41. Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P
  • 42.
  • 43.
  • 44. Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F
  • 45. Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F
  • 46. Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F
  • 47. Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F F
  • 48. Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F F F T
  • 49. Example 4: P  Q, Q  R, ~S  V / V  P Pr1 Pr2 Pr3 C P  Q Q  R ~S  V V  P F F F T F F F F T
  • 50.
  • 51.
  • 52.
  • 53.
  • 54.
  • 55.
  • 56.
  • 57.
  • 58.
  • 59.
  • 60.
  • 61.
  • 62.
  • 63.
  • 64.
  • 65.
  • 66.
  • 67.
  • 68. Indirect-tables to determine if a set of formulae is satisfiable:
  • 69.
  • 70.
  • 71.
  • 72. Example: P  Q, ~P  Q P  Q ~P  Q
  • 73. Example: P  Q, ~P  Q P  Q ~P  Q T T
  • 74. Example: P  Q, ~P  Q P  Q ~P  Q T T F F T F
  • 75. Example: P  Q, ~P  Q Satisfiable P  Q ~P  Q T T F F T F
  • 76. Example: P  Q, P  ~Q P  Q P  ~Q
  • 77. Example: P  Q, P  ~Q P  Q P  ~Q T T
  • 78. Example: P  Q, P  ~Q P  Q P  ~Q T T T T F
  • 79. Example: P  Q, P  ~Q P  Q P  ~Q T T T F T T F
  • 80. Example: P  Q, P  ~Q P  Q P  ~Q T T T F T T F F
  • 81. Example: P  Q, P  ~Q Unsatisfiable P  Q P  ~Q T T T F T T F F
  • 82. Example: P  ~Q, P  Q P  ~Q P  Q T T T F T F F T F
  • 83. Example: P  ~Q, P  Q P  ~Q P  Q T T T T T F T F F T F
  • 84. Example: P  ~Q, P  Q P  ~Q P  Q T F T T T T F T F F T F
  • 85. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T F T F F T F
  • 86. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T F F T F F T F
  • 87. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T F F T F F T F
  • 88. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T F
  • 89. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T T F F T F
  • 90. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F F F T F
  • 91. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T F F T F
  • 92. Example: P  ~Q, P  Q P  ~Q P  Q T F F T T T T T T T F F T F F T T F F T F
  • 93. Example: P  ~Q, P  Q Satisfiable P  ~Q P  Q T F F T T T T T T T F F T F F T T F F T F
  • 94. Summary of indirect-table tests: Test Procedure Results Satisfiability Place T under the main connective of each formula If there is at least one row where every formula can be T, the set is satisfiable. Validity Place T under every premise, F under conclusion If there is a row where premises are true and conclusion is false, argument is invalid.
  • 95.