Dl wright -section 3.7
-
Upload
thinkmathematically -
Category
Spiritual
-
view
542 -
download
1
Transcript of Dl wright -section 3.7
![Page 1: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/1.jpg)
Unit II LOGICSection 3.7: Argument and Truth Tables
![Page 2: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/2.jpg)
What is an argument???
An argument consists of TWO parts!1. Premises given statements2. Conclusion decision reached
![Page 3: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/3.jpg)
True or not…that is the QUESTION!• Valid Argument : If premises are true,
the conclusion is true
• Invalid Argument (fallacy): argument that isn’t true
![Page 4: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/4.jpg)
Testing the Validity of a Statement• Use TRUTH TABLES!!!
• An argument is valid if the statement is a tautology (basically the last column of the truth table is true)
![Page 5: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/5.jpg)
Types of Valid ArgumentsReasoning Symbolic Representation
Direct 𝑝⟶𝑞 𝑝 ∴ 𝑞
Contrapositive 𝑝⟶𝑞 ~𝑞 ∴ ~𝑝
Disjunctive 𝑝∨𝑞 𝑝∨𝑞 ~𝑝 ∴ 𝑞 ~𝑞 ∴ 𝑝
Transitive
𝑝⟶𝑞 𝑞 ⟶𝑟 ∴ 𝑝⟶𝑟 ∴ ~𝑟⟶~𝑝
![Page 6: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/6.jpg)
Types of Invalid ArgumentsReasoning Symbolic Representation
Fallacy of the Converse 𝑝⟶𝑞 𝑞 ∴ 𝑝
Fallacy of the Inverse 𝑝⟶𝑞 ~𝑝 ∴ ~𝑞
Misuse of Disjunctive Reasoning
𝑝∨𝑞 𝑝∨𝑞 𝑝 ∴ ~𝑞 𝑞 ∴ ~𝑝 Misuse of Transitive Reasoning
𝑝⟶𝑞 𝑞 ⟶𝑟 ∴ 𝑟⟶𝑝 ∴ ~𝑝⟶~𝑟
![Page 7: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/7.jpg)
Example :
𝒑 𝒒 ~𝒑 ~𝒒 𝒑⟶𝒒 ሺ𝒑⟶𝒒ሻ∧~𝒑 ሾሺ𝒑⟶𝒒ሻ∧~𝒑ሿ⟶~𝒒
1.
𝑝⟶𝑞 ~𝑝 ∴ ~𝑞 ሾሺ𝒑⟶𝒒ሻ∧~𝒑ሿ⟶~𝒒
![Page 8: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/8.jpg)
SOLUTION Example :
𝒑 𝒒 ~𝒑 ~𝒒 𝒑⟶𝒒 ሺ𝒑⟶𝒒ሻ∧~𝒑 ሾሺ𝒑⟶𝒒ሻ∧~𝒑ሿ⟶~𝒒
T T
T F
F T
T F
1. Fallacy of inverse invalid 𝑝⟶𝑞 ~𝑝 ∴ ~𝑞
Solution using TRUTH TABLE:
![Page 9: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/9.jpg)
SOLUTION Example :
𝒑 𝒒 ~𝒑 ~𝒒 𝒑⟶𝒒 ሺ𝒑⟶𝒒ሻ∧~𝒑 ሾሺ𝒑⟶𝒒ሻ∧~𝒑ሿ⟶~𝒒
T T F F
T F F T
F T T F
F F T T
1. Fallacy of inverse invalid 𝑝⟶𝑞 ~𝑝 ∴ ~𝑞
Solution using TRUTH TABLE:
![Page 10: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/10.jpg)
SOLUTION Example :
𝒑 𝒒 ~𝒑 ~𝒒 𝒑⟶𝒒 ሺ𝒑⟶𝒒ሻ∧~𝒑 ሾሺ𝒑⟶𝒒ሻ∧~𝒑ሿ⟶~𝒒
T T F F T
T F F T F
F T T F T
F F T T T
1. Fallacy of inverse invalid 𝑝⟶𝑞 ~𝑝 ∴ ~𝑞
Solution using TRUTH TABLE:
![Page 11: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/11.jpg)
SOLUTION Example :
𝒑 𝒒 ~𝒑 ~𝒒 𝒑⟶𝒒 ሺ𝒑⟶𝒒ሻ∧~𝒑 ሾሺ𝒑⟶𝒒ሻ∧~𝒑ሿ⟶~𝒒
T T F F T F
T F F T F F
F T T F T T
F F T T T T
1. Fallacy of inverse invalid 𝑝⟶𝑞 ~𝑝 ∴ ~𝑞
Solution using TRUTH TABLE:
![Page 12: Dl wright -section 3.7](https://reader035.fdocuments.us/reader035/viewer/2022062319/5577df11d8b42a7b7b8b4a4b/html5/thumbnails/12.jpg)
SOLUTION Example :
𝒑 𝒒 ~𝒑 ~𝒒 𝒑⟶𝒒 ሺ𝒑⟶𝒒ሻ∧~𝒑 ሾሺ𝒑⟶𝒒ሻ∧~𝒑ሿ⟶~𝒒
T T F F T F T
T F F T F F F
F T T F T T T
F F T T T T T
1. Fallacy of inverse invalid 𝑝⟶𝑞 ~𝑝 ∴ ~𝑞
Solution using TRUTH TABLE:
Since the second row of the last column is FALSE, the statement is a fallacy, or INVALID