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Use the change of quantifier rule together with the eighteen rules of inference to derive the conclusions of the following symbolized argument. Do not use eithe conditional proof or indirect proof. NOTE: Throughout, in the proof checker tool, CQ, which stands for Change of Quantifier Rule, is used instead of QN, which stands for Quantifier Negation Rule. Please remember to use CQ whenever you wish to apply the Quantifier Negation Rule, QN. A B C Xx (3x) (x) 3 CQ MP Dist 1 2 3 UI MT DN UG HS Trans PREMISE ● PREMISE (x) Ax (3x)~Bx PREMISE DV EI ~(x)Bx (3x)~Cx EG Id DS CD Impl Equiv ( ) { } Simp Conj Add Exp Taut ACP CONCLUSION (x)Cx (3x) ~ Ax DM CP [] Com AIP Assoc IP

Use the change of quantifier rule together with the eighteen rules of inference to derive the conclusions of the following symbolized argument. Do not use eithe conditional proof or indirect proof. NOTE: Throughout, in the proof checker tool, CQ, which stands for Change of Quantifier Rule, is used instead of QN, which stands for Quantifier Negation Rule. Please remember to use CQ whenever you wish to apply the Quantifier Negation Rule, QN. A B C Xx (3x) (x) 3 CQ MP Dist 1 2 3 UI MT DN UG HS Trans PREMISE ● PREMISE (x) Ax (3x)~Bx PREMISE DV EI ~(x)Bx (3x)~Cx EG Id DS CD Impl Equiv ( ) { } Simp Conj Add Exp Taut ACP CONCLUSION (x)Cx (3x) ~ Ax DM CP [] Com AIP Assoc IP

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Use the change of quantifier rule together with the eighteen rules of inference to derive the conclusions of the following symbolized argument. Do not use either conditional proof or indirect proof. **NOTE:** Throughout, in the proof checker tool, **CQ**, which stands for **Change of Quantifier Rule**, is used instead of **QN**, which stands for **Quantifier Negation Rule**. Please remember to use **CQ** whenever you wish to apply the **Quantifier Negation Rule, QN**. --- ### Symbols and Operators - `(∃x)`: There exists an x - `(x)`: For all x - `~`: Not - `•`: And - `∨`: Or - `⊃`: Implies - `≡`: If and only if - `= ÷`: Not equal - `()`: Parentheses - `{}`: Set brackets - `[]`: Square brackets ### Rules and Inference Abbreviations - **CQ**: Change of Quantifier - **UI**: Universal Instantiation - **UG**: Universal Generalization - **EI**: Existential Instantiation - **EG**: Existential Generalization - **Id**: Identity - **MP**: Modus Ponens - **MT**: Modus Tollens - **HS**: Hypothetical Syllogism - **DS**: Disjunctive Syllogism - **CD**: Constructive Dilemma - **Simp**: Simplification - **Conj**: Conjunction - **Add**: Addition - **DM**: De Morgan’s Theorems - **Com**: Commutation - **Assoc**: Association - **Dist**: Distribution - **DN**: Double Negation - **Trans**: Transposition - **Impl**: Material Implication - **Equiv**: Equivalence - **Exp**: Exportation - **Taut**: Tautology - **ACP**: Assumption for Conditional Proof - **CP**: Conditional Proof - **AIP**: Assumption for Indirect Proof - **IP**: Indirect Proof --- ### Proof Steps 1. **Premise (1):** `(x)Ax ⊃ (∃x)~Bx` 2
Transcribed Image Text:Use the change of quantifier rule together with the eighteen rules of inference to derive the conclusions of the following symbolized argument. Do not use either conditional proof or indirect proof. **NOTE:** Throughout, in the proof checker tool, **CQ**, which stands for **Change of Quantifier Rule**, is used instead of **QN**, which stands for **Quantifier Negation Rule**. Please remember to use **CQ** whenever you wish to apply the **Quantifier Negation Rule, QN**. --- ### Symbols and Operators - `(∃x)`: There exists an x - `(x)`: For all x - `~`: Not - `•`: And - `∨`: Or - `⊃`: Implies - `≡`: If and only if - `= ÷`: Not equal - `()`: Parentheses - `{}`: Set brackets - `[]`: Square brackets ### Rules and Inference Abbreviations - **CQ**: Change of Quantifier - **UI**: Universal Instantiation - **UG**: Universal Generalization - **EI**: Existential Instantiation - **EG**: Existential Generalization - **Id**: Identity - **MP**: Modus Ponens - **MT**: Modus Tollens - **HS**: Hypothetical Syllogism - **DS**: Disjunctive Syllogism - **CD**: Constructive Dilemma - **Simp**: Simplification - **Conj**: Conjunction - **Add**: Addition - **DM**: De Morgan’s Theorems - **Com**: Commutation - **Assoc**: Association - **Dist**: Distribution - **DN**: Double Negation - **Trans**: Transposition - **Impl**: Material Implication - **Equiv**: Equivalence - **Exp**: Exportation - **Taut**: Tautology - **ACP**: Assumption for Conditional Proof - **CP**: Conditional Proof - **AIP**: Assumption for Indirect Proof - **IP**: Indirect Proof --- ### Proof Steps 1. **Premise (1):** `(x)Ax ⊃ (∃x)~Bx` 2
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