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On the basis of this summation, should the defendant be found guilty or not guilty? c) Hypothesis: (Conditional Proof) d) Hypothesis: P→ R Q→ → R :. (PVQ) R ¬(PAQ) ¬R → Q P→ R :. R

On the basis of this summation, should the defendant be found guilty or not guilty? c) Hypothesis: (Conditional Proof) d) Hypothesis: P→ R Q→ → R :. (PVQ) R ¬(PAQ) ¬R → Q P→ R :. R

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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answer the c and d based on the guven example

Example Prove P→(Q→R) -SVP Q ...S→R Proof Statement 1. P→(Q→R) 2. -SVP 3. Q 4. S/..R 5. P 6. Q→ R 7. R Reason Hypothesis Hypothesis Hypothesis Conditional Proof (2) & (4) Disjunctive Syllogism (1) & (5) Modus Ponens (3) & (6) Modus Ponens
Transcribed Image Text:Example Prove P→(Q→R) -SVP Q ...S→R Proof Statement 1. P→(Q→R) 2. -SVP 3. Q 4. S/..R 5. P 6. Q→ R 7. R Reason Hypothesis Hypothesis Hypothesis Conditional Proof (2) & (4) Disjunctive Syllogism (1) & (5) Modus Ponens (3) & (6) Modus Ponens
Supply the reasons for each step needed to show that the following argument is valid. b) At the end of a long and heated trial, the defense attorney sums up his case as follows: "If my client were guilty (G), then he must have been at the scene of the crime (A). It is certainly not true that he was at the scene of the crime and at the same time was out of town (O). Now, if the witness who identified my client as being out of town was not mistaken (~M), then my client must have been out of town. But, the Prosecution Attorney was not able to prove that the witness was mistaken. Therefore, my client is not guilty." On the basis of this summation, should the defendant be found guilty or not guilty? c) Hypothesis: (Conditional Proof) d) Hypothesis: P R Q :. (PV Q) → R → R e) Hypothesis: P P→ Q SVR R→ ¬Q : SVT PROOF 1. P 2. P→ Q 3. SVR 4. R→ ¬Q 5.Q 6.¬R 7.S 8. SVT REASON ¬(P^Q) ¬R → Q P→ R :R f) Hypothesis: (Indirect Proof) ¬QVR P→ ¬R Q : ¬P PROOF 1. ¬Q VR 2.P→ ¬R 3. Q 4.P/: f R 5.Q 6. R 7. ¬P 8. PAP 9.f REASON
Transcribed Image Text:Supply the reasons for each step needed to show that the following argument is valid. b) At the end of a long and heated trial, the defense attorney sums up his case as follows: "If my client were guilty (G), then he must have been at the scene of the crime (A). It is certainly not true that he was at the scene of the crime and at the same time was out of town (O). Now, if the witness who identified my client as being out of town was not mistaken (~M), then my client must have been out of town. But, the Prosecution Attorney was not able to prove that the witness was mistaken. Therefore, my client is not guilty." On the basis of this summation, should the defendant be found guilty or not guilty? c) Hypothesis: (Conditional Proof) d) Hypothesis: P R Q :. (PV Q) → R → R e) Hypothesis: P P→ Q SVR R→ ¬Q : SVT PROOF 1. P 2. P→ Q 3. SVR 4. R→ ¬Q 5.Q 6.¬R 7.S 8. SVT REASON ¬(P^Q) ¬R → Q P→ R :R f) Hypothesis: (Indirect Proof) ¬QVR P→ ¬R Q : ¬P PROOF 1. ¬Q VR 2.P→ ¬R 3. Q 4.P/: f R 5.Q 6. R 7. ¬P 8. PAP 9.f REASON
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