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Use the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof. A B C m x (3x) (x) 3 CQ MP Dist 1 2 3 UI MT DN UG ● EI HS DS Trans Impl PREMISE (3x) (Ax ~Cx) PREMISE DV PREMISE (x) [Ax (Bx v Cx)] EG Id CD Equiv CONCLUSION (3x)Bx = # () { Simp Exp Conj Add Taut ACP } [ ] DM CP Com AIP Assoc IP

Use the eighteen rules of inference to derive the conclusion of the following symbolized argument. Do not use either conditional proof or indirect proof. A B C m x (3x) (x) 3 CQ MP Dist 1 2 3 UI MT DN UG ● EI HS DS Trans Impl PREMISE (3x) (Ax ~Cx) PREMISE DV PREMISE (x) [Ax (Bx v Cx)] EG Id CD Equiv CONCLUSION (3x)Bx = # () { Simp Exp Conj Add Taut ACP } [ ] 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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**Using the Eighteen Rules of Inference** To derive the conclusion of the following symbolized argument, do not use either conditional proof or indirect proof. ### Symbolized Argument 1. **Premise**: \((x)[Ax \supset (Bx \lor Cx)]\) 2. **Premise**: \((\exists x)(Ax \cdot \sim Cx)\) **Conclusion**: \((\exists x)Bx\) 3. **Provide the necessary steps here to complete the derivation using the rules of inference.** ### Explanation of Symbols and Rules - \( (x) \): Universal quantifier (for all x) - \( (\exists x) \): Existential quantifier (there exists an x) - \( \sim \): Not - \( \lor \): Or - \( \cdot \): And - \( \supset \): Implies - \( = \): Equals - \( \neq \): Does not equal ### Inference Rules Overview - **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 Laws - **Com**: Commutation - **Assoc**: Association - **Dist**: Distribution - **DN**: Double Negation - **Trans**: Transposition - **Impl**: Implication - **Equiv**: Equivalence - **Exp**: Exportation - **Taut**: Tautology - **ACP**: Assumption for Conditional Proof - **CP**: Conditional Proof - **AIP**: Assumption for Indirect Proof - **IP**: Indirect Proof ### Instruction Fill in line 3 with the necessary logical steps to reach the conclusion. Use the rules of inference listed above without employing conditional or indirect
Transcribed Image Text:**Using the Eighteen Rules of Inference** To derive the conclusion of the following symbolized argument, do not use either conditional proof or indirect proof. ### Symbolized Argument 1. **Premise**: \((x)[Ax \supset (Bx \lor Cx)]\) 2. **Premise**: \((\exists x)(Ax \cdot \sim Cx)\) **Conclusion**: \((\exists x)Bx\) 3. **Provide the necessary steps here to complete the derivation using the rules of inference.** ### Explanation of Symbols and Rules - \( (x) \): Universal quantifier (for all x) - \( (\exists x) \): Existential quantifier (there exists an x) - \( \sim \): Not - \( \lor \): Or - \( \cdot \): And - \( \supset \): Implies - \( = \): Equals - \( \neq \): Does not equal ### Inference Rules Overview - **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 Laws - **Com**: Commutation - **Assoc**: Association - **Dist**: Distribution - **DN**: Double Negation - **Trans**: Transposition - **Impl**: Implication - **Equiv**: Equivalence - **Exp**: Exportation - **Taut**: Tautology - **ACP**: Assumption for Conditional Proof - **CP**: Conditional Proof - **AIP**: Assumption for Indirect Proof - **IP**: Indirect Proof ### Instruction Fill in line 3 with the necessary logical steps to reach the conclusion. Use the rules of inference listed above without employing conditional or indirect
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