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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
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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**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
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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