Create a proof for the following argument, using the implication rules and replacement rules. 1. (A • B) v (D · F) 2. F |A·B 3. Create a proof for the following argument. 1. -C 2. (C v M) v N /M v N 1. C 2. (C v M) v N / MVN 3. Create a proof for the following argument. 1. G 2. ~Cv (G v ~K) | (C • K) 3. Create a proof for the following argument. 1. ~(L v M) = (H v K) 2. L.M |HVK 3. Create a proof for the following argument. 1. (F> G) • (C > D) 2. ~(~C• F) 3. D 4.
Create a proof for the following argument, using the implication rules and replacement rules. 1. (A • B) v (D · F) 2. F |A·B 3. Create a proof for the following argument. 1. -C 2. (C v M) v N /M v N 1. C 2. (C v M) v N / MVN 3. Create a proof for the following argument. 1. G 2. ~Cv (G v ~K) | (C • K) 3. Create a proof for the following argument. 1. ~(L v M) = (H v K) 2. L.M |HVK 3. Create a proof for the following argument. 1. (F> G) • (C > D) 2. ~(~C• F) 3. D 4.
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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Question
![**Transcription and Explanation:**
This image provides several logical proofs using implication rules and replacement rules. Each segment outlines a different argument to be proven, with numbered steps and spaces for completing the proofs.
---
**Section 1:**
- **Argument to Prove:**
\((A \cdot B) \lor (D \cdot F)\)
- **Given Statements:**
1. \(\sim F\)
2. \(A \cdot B\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 2:**
- **Argument to Prove:**
\(M \lor N\)
- **Given Statements:**
1. \(\sim C\)
2. \((C \lor M) \lor N\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 3:**
- **Argument to Prove:**
\(C \cdot K\)
- **Given Statements:**
1. \(\sim G\)
2. \(\sim C \lor (G \lor \sim K)\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 4:**
- **Argument to Prove:**
\(H \lor K\)
- **Given Statements:**
1. \(\sim (L \lor M) \supset (H \lor K)\)
2. \(\sim L \cdot \sim M\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 5:**
- **Argument to Prove:**
\(G\)
- **Given Statements:**
1. \((F \supset G) \cdot (C \supset D)\)
2. \(\sim (\sim C \cdot \sim F)\)
3. \(\sim D\)
- **Proof Layout:**
- Step 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F07cd9715-7e40-46aa-8a30-5a2ee2cd1f05%2F973f82ff-9f5f-473d-9a43-efd48049adc0%2Fdx91uq5_processed.png&w=3840&q=75)
Transcribed Image Text:**Transcription and Explanation:**
This image provides several logical proofs using implication rules and replacement rules. Each segment outlines a different argument to be proven, with numbered steps and spaces for completing the proofs.
---
**Section 1:**
- **Argument to Prove:**
\((A \cdot B) \lor (D \cdot F)\)
- **Given Statements:**
1. \(\sim F\)
2. \(A \cdot B\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 2:**
- **Argument to Prove:**
\(M \lor N\)
- **Given Statements:**
1. \(\sim C\)
2. \((C \lor M) \lor N\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 3:**
- **Argument to Prove:**
\(C \cdot K\)
- **Given Statements:**
1. \(\sim G\)
2. \(\sim C \lor (G \lor \sim K)\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 4:**
- **Argument to Prove:**
\(H \lor K\)
- **Given Statements:**
1. \(\sim (L \lor M) \supset (H \lor K)\)
2. \(\sim L \cdot \sim M\)
- **Proof Layout:**
- Step 3 has a blank to fill with the derived logical conclusion.
- Two empty boxes for rule numbers used.
---
**Section 5:**
- **Argument to Prove:**
\(G\)
- **Given Statements:**
1. \((F \supset G) \cdot (C \supset D)\)
2. \(\sim (\sim C \cdot \sim F)\)
3. \(\sim D\)
- **Proof Layout:**
- Step 4
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