Use the first thirteen rules of inference to derive the conclusions of the symbolized arguments. Please show all work and all the steps. Please answer as quickly as possible. The image contains a logical deduction table used to derive conclusions from provided premises using inference rules. It is structured into several components:### Structure- **Variable and Operator Symbols:** - **H, N, P, Q, R, U**: Variables. - **~**: Not. - **•**: And. - **→**: If...then (implication). - **=**: Equivalent. - **() {} []**: Parentheses for grouping.- **Inference Rules and Abbreviations:** - **MP**: Modus Ponens - **MT**: Modus Tollens - **HS**: Hypothetical Syllogism - **DS**: Disjunctive Syllogism - **CD**: Constructive Dilemma - **Simp**: Simplification - **Conj**: Conjunction - **Add**: Addition - **DN**: Double Negation - **Trans**: Transposition - **Impl**: Implication - **Equiv**: Equivalence - **Exp**: Exportation - **Taut**: Tautology - **DM**: De Morgan's Theorems - **Com**: Commutation - **Assoc**: Association - **Dist**: Distribution - **ACP**: Assumptions for Conditional Proof - **CP**: Conditional Proof - **AIP**: Assumptions for Indirect Proof - **IP**: Indirect Proof### Logical Proof Structure1. **Premise 1**: \(\sim (U \lor R)\)2. **Premise 2**: \((\sim R \lor N) \supset (P \cdot H)\)3. **Premise 3**: - **Given Premise**: \(Q \supset \sim H\) - **Conclusion to Derive**: \(\sim Q\)4. **Empty Premise Line 4**: - Reserved for further steps or conclusions based on the inference rules applied.### ExplanationThe table lists premises and sets up the logical environment for deriving conclusions through the application of inference rules. The goal

Use the first thirteen rules of inference to derive the conclusions of the symbolized HN P Q RU ~ MP Dist 2 3 4 ● D V = MT DN HS DS Trans Impl 4 PREMISE ~ (U v R) (){} [] PREMISE (~RVN) (P. H) PREMISE QU ~H PREMISE CD Equiv CONCLUSION Simp Conj Exp Taut Add ACP DM CP Com Assoc AIP IP

Use the first thirteen rules of inference to derive the conclusions of the symbolized HN P Q RU ~ MP Dist 2 3 4 ● D V = MT DN HS DS Trans Impl 4 PREMISE ~ (U v R) (){} [] PREMISE (~RVN) (P. H) PREMISE QU ~H PREMISE CD Equiv CONCLUSION Simp Conj Exp Taut Add ACP DM CP Com Assoc AIP IP

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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