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English Chapter 2: Logic: Inference

The document summarizes 8 rules of logical inference: 1. Addition 2. Simplification 3. Modus Ponens 4. Modus Tollens 5. Disjunctive Syllogism 6. Hypothetical Syllogism 7. Constructive Dilemma 8. Destructive Dilemma Each rule is explained through a truth table that shows how the conclusion follows from the premises.

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Putri Fatmasari
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29 views4 pages

English Chapter 2: Logic: Inference

The document summarizes 8 rules of logical inference: 1. Addition 2. Simplification 3. Modus Ponens 4. Modus Tollens 5. Disjunctive Syllogism 6. Hypothetical Syllogism 7. Constructive Dilemma 8. Destructive Dilemma Each rule is explained through a truth table that shows how the conclusion follows from the premises.

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Putri Fatmasari
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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ENGLISH CHAPTER 2 : LOGIC

PUTRI FATMASARI
105361103618
2018B

INFERENCE

1. Addition
𝒑 → (𝒑 ∨ 𝒒)

𝑝 𝑞 (𝑝 ∨ 𝑞) 𝑝 → (𝑝 ∨ 𝑞)
T T T T
T F T T
F T T T
F F F T

2. Simplification
(𝒑 ∨ 𝒒 → 𝒑)

𝑝 𝑞 (𝑝 ∨ 𝑞) (𝑝 ∨ 𝑞 → 𝑝)
T T T T
T F T T
F T T F
F F F T
3. Modus Ponens

[𝒑 ∧ (𝒑 → 𝒒)] → 𝒒

𝑝 𝑞 (𝑝 → 𝑞) [𝑝 ∧ (𝑝 → 𝑞)] [𝑝 ∧ (𝑝 → 𝑞)] → 𝑞
T T T T T
T F F F T
F T T F T
F F T F T

4. Modus Tollens

[~𝒒 ∧ (𝒑 → 𝒒)] → ~𝒑

𝑝 𝑞 ~𝑝 ~𝑞 (𝑝 → 𝑞) [~𝑞 ∧ (𝑝 → 𝑞)] [~𝑞 ∧ (𝑝 → 𝑞)] → ~𝑝


T T F F T F T
T F F T F F T
F T T F T F T
F F T T T T T

5. Disjunctive Syllogism

[(𝒑 ∨ 𝒒) ∧ ~𝒑] → 𝒒)

𝑝 𝑞 ~𝑝 (𝑝 ∨ 𝑞) [(𝑝 ∨ 𝑞) ∧ ~𝑝] [(𝑝 ∨ 𝑞) ∧ ~𝑝] → 𝑞)


T T F T F T
T F F T F T
F T T T T T
F F T F F T
6. Hypothetical Syllogism

[(𝒑 → 𝒒) ∧ (𝒒 → 𝒓)] → (𝒑 → 𝒓)

𝑝 𝑞 𝑟 (𝑝 → 𝑞) (𝑞 → 𝑟) (𝑝 → 𝑟) [(𝑝 → 𝑞) ∧ (𝑞 → 𝑟)] [(𝑝 → 𝑞) ∧ (𝑞 → 𝑟)] → (𝑝 → 𝑟)


T T T T T T T T
T T F T F F F T
T F T F T T F T
T F F F T F F T
F T T T T T T T
F T F T F T F T
F F T T T T T T
F F F T T T T T

7. Constructive Dilemma

[[(𝒑 → 𝒒) ∧ (𝒓 → 𝒔)] ∧ (𝒑 ∨ 𝒓)] → (𝒒 ∨ 𝒔)

𝑝 𝑞 𝑟 𝑠 (𝑝 → 𝑞) (𝑟 → 𝑠) (𝑝 ∨ 𝑟) (𝑞 ∨ 𝑠) (𝑝 → 𝑞) ∧ (𝑟 → 𝑠) [[(𝑝 → 𝑞) ∧ (𝑟 → 𝑠)] ∧ (𝑝 ∨ 𝑟)] [[(𝑝 → 𝑞) ∧ (𝑟 → 𝑠)] ∧ (𝑝 ∨ 𝑟)] → (𝑞 ∨ 𝑠)


T T T T T T T T T T T
T T T F T F T T F F T
T T F T T T T T T T T
T T F F T T T T T T T
T F T T F T T T F F T
T F T F F F T F F F T
T F F T F T T T F F T
T F F F F T T F F F T
F T T T T T T T T T T
F T T F T F T T F F T
F T F T T T F T T F T
F T F F T T F T T F T
F F T T T T T T T T T
F F T F T F T F F F T
F F F T T T F T T F T
F F F F T T F F T F T
8. Destructive Dilemma

[[(𝒑 → 𝒒) ∧ (𝒓 → 𝒔)] ∧ (~𝒒 ∨ ~𝒔)] → (~𝒑 ∨ ~𝒓)

𝑝 𝑞 𝑟 𝑠 ~𝑝 ~𝑞 ~𝑟 ~𝑠 (𝑝 → 𝑞) (𝑟 → 𝑠) (~𝑞 ∨ ~𝑠) (~𝑝 ∨ ~𝑟) (𝑝 → 𝑞) ∧ (𝑟 → 𝑠) [[(𝑝 → 𝑞) ∧ (𝑟 → 𝑠)] ∧ (~𝑞 ∨ ~𝑠)] [[(𝑝 → 𝑞) ∧ (𝑟 → 𝑠)] ∧ (~𝑞 ∨ ~𝑠)] → (~𝑝 ∨ ~𝑟)
T T T T F F F F T T F F T F T
T T T F F F F T T F T F F F T
T T F T F F T F T T F T T F T
T T F F F F T T T T T T T T T
T F T T F T F F F T T F F F T
T F T F F T F T F F T F F F T
T F F T F T T F F T T T F F T
T F F F F T T T F T T T F F T
F T T T T F F F T T F T T F T
F T T F T F F T T F T T F F T
F T F T T F T F T T F T T F T
F T F F T F T T T T T T T T T
F F T T T T F F T T T T T T T
F F T F T T F T T F T T F F T
F F F T T T T F T T T T T T T
F F F F T T T T T T T T T T T

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