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Use either indirect proof or conditional proof (or both) and the eighteen rules NOTE: Include the numbers of the first and last indented premises when listing you identify with CP or IP. A B C D E 2 MP Dist 1 2 3 MT DN V = () HS Trans PREMISE (A v B) > C PREMISE (~A v D) DE PREMISE DS Impl CD Equiv CONCLUSION CVE Simp Conj Add Taut ACP Exp DM CP

Use either indirect proof or conditional proof (or both) and the eighteen rules NOTE: Include the numbers of the first and last indented premises when listing you identify with CP or IP. A B C D E 2 MP Dist 1 2 3 MT DN V = () HS Trans PREMISE (A v B) > C PREMISE (~A v D) DE PREMISE DS Impl CD Equiv CONCLUSION CVE Simp Conj Add Taut ACP Exp DM CP

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 either indirect proof or conditional proof (or both)and the eighteen rules of inference to derive the conclusions of the symbolized arguments. Please answer as quickly as possible and show all steps and how to get those steps.

**Instructions for Using Indirect or Conditional Proof Techniques in Logic** --- ### Logical Symbols and Rules #### Symbols: - **~**: Negation - **∙**: Conjunction - **∨**: Disjunction - **⊃**: Conditional - **=**: Biconditional - **Parentheses**: Indicate grouping - **Braces**, **Brackets**: Used similarly for additional clarity and grouping #### Eighteen Rules of Inference and Equivalence: 1. **MP**: Modus Ponens 2. **MT**: Modus Tollens 3. **HS**: Hypothetical Syllogism 4. **DS**: Disjunctive Syllogism 5. **CD**: Constructive Dilemma 6. **Simp**: Simplification 7. **Conj**: Conjunction 8. **Add**: Addition 9. **DM**: De Morgan’s Laws 10. **Dist**: Distribution 11. **DN**: Double Negation 12. **Trans**: Transposition 13. **Impl**: Implication 14. **Equiv**: Equivalence 15. **Exp**: Exportation 16. **Taut**: Tautology 17. **ACP**: Assumption for Conditional Proof 18. **CP**: Conditional Proof ### Premises and Conclusions 1. **Premise 1**: \((A \vee B) ⊃ C\) 2. **Premise 2**: \((\sim A \vee D) ⊃ E\) **Conclusion**: \(C \vee E\) 3. **Premise**: (Blank for further derivation) --- #### Additional Instructions: - **Note**: Include the numbers of the first and last indented premises when listing proofs identified with Conditional Proof (CP) or Indirect Proof (IP). This educational layout provides a framework for constructing proofs in logical arguments using formal methods.
Transcribed Image Text:**Instructions for Using Indirect or Conditional Proof Techniques in Logic** --- ### Logical Symbols and Rules #### Symbols: - **~**: Negation - **∙**: Conjunction - **∨**: Disjunction - **⊃**: Conditional - **=**: Biconditional - **Parentheses**: Indicate grouping - **Braces**, **Brackets**: Used similarly for additional clarity and grouping #### Eighteen Rules of Inference and Equivalence: 1. **MP**: Modus Ponens 2. **MT**: Modus Tollens 3. **HS**: Hypothetical Syllogism 4. **DS**: Disjunctive Syllogism 5. **CD**: Constructive Dilemma 6. **Simp**: Simplification 7. **Conj**: Conjunction 8. **Add**: Addition 9. **DM**: De Morgan’s Laws 10. **Dist**: Distribution 11. **DN**: Double Negation 12. **Trans**: Transposition 13. **Impl**: Implication 14. **Equiv**: Equivalence 15. **Exp**: Exportation 16. **Taut**: Tautology 17. **ACP**: Assumption for Conditional Proof 18. **CP**: Conditional Proof ### Premises and Conclusions 1. **Premise 1**: \((A \vee B) ⊃ C\) 2. **Premise 2**: \((\sim A \vee D) ⊃ E\) **Conclusion**: \(C \vee E\) 3. **Premise**: (Blank for further derivation) --- #### Additional Instructions: - **Note**: Include the numbers of the first and last indented premises when listing proofs identified with Conditional Proof (CP) or Indirect Proof (IP). This educational layout provides a framework for constructing proofs in logical arguments using formal methods.
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