1is proor oved) systen 1.А — В P 2.А P[for A → B] 3.А — (В — А) Aхiom 1 4.В → A 2, 3, MP 5.А — (В — А) 2 — 4, СР 6.(А — В) — (В — A) 1,5, СР
1is proor oved) systen 1.А — В P 2.А P[for A → B] 3.А — (В — А) Aхiom 1 4.В → A 2, 3, MP 5.А — (В — А) 2 — 4, СР 6.(А — В) — (В — A) 1,5, СР
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Proof for an F-L Axiom System:**
1. \( A \to B \)
- *Assumption (P)*
2. \( A \)
- *Assumption [for \( A \to B \)]*
3. \( A \to (B \to A) \)
- *Axiom 1*
4. \( B \to A \)
- *From 2, 3 using Modus Ponens (MP)*
5. \( A \to (B \to A) \)
- *From 2, 4 using Conditional Proof (CP)*
6. \( (A \to B) \to (B \to A) \)
- *From 1, 5 using Conditional Proof (CP)*
**Question: Which is most accurate?**
- [ ] Correct proof
- [ ] Incorrect at line 2
- [ ] Incorrect at line 5
- [ ] Incorrect at line 6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff43fe492-0086-4aac-90eb-2b796e708e5e%2F9b231191-3421-4884-a5e5-9b16c47a6887%2F2q24vv_processed.png&w=3840&q=75)
Transcribed Image Text:**Proof for an F-L Axiom System:**
1. \( A \to B \)
- *Assumption (P)*
2. \( A \)
- *Assumption [for \( A \to B \)]*
3. \( A \to (B \to A) \)
- *Axiom 1*
4. \( B \to A \)
- *From 2, 3 using Modus Ponens (MP)*
5. \( A \to (B \to A) \)
- *From 2, 4 using Conditional Proof (CP)*
6. \( (A \to B) \to (B \to A) \)
- *From 1, 5 using Conditional Proof (CP)*
**Question: Which is most accurate?**
- [ ] Correct proof
- [ ] Incorrect at line 2
- [ ] Incorrect at line 5
- [ ] Incorrect at line 6
![**Hilbert-Ackerman Axioms (H-A):**
1. \( A \lor A \to A \)
2. \( A \to A \lor B \)
3. \( A \lor B \to B \lor A \)
4. \( (A \to B) \to (C \lor A \to C \lor B) \)
**Proof Rules:**
- MP (Modus Ponens)
- \( A \to B \equiv \neg A \lor B \)
---
**Question:**
Is the following proof of the given well-formed formula (wff) correct?
\[ \neg A \to (A \to B) \]
**Proof:**
1. \( \neg A \to (\neg A \lor B) \)
2. \( \neg A \to (A \to B) \)
QED
---
**Answer Options:**
- ○ True
- ○ False
- ○ No idea
- ○ Where am I?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff43fe492-0086-4aac-90eb-2b796e708e5e%2F9b231191-3421-4884-a5e5-9b16c47a6887%2Fgsrz6e_processed.png&w=3840&q=75)
Transcribed Image Text:**Hilbert-Ackerman Axioms (H-A):**
1. \( A \lor A \to A \)
2. \( A \to A \lor B \)
3. \( A \lor B \to B \lor A \)
4. \( (A \to B) \to (C \lor A \to C \lor B) \)
**Proof Rules:**
- MP (Modus Ponens)
- \( A \to B \equiv \neg A \lor B \)
---
**Question:**
Is the following proof of the given well-formed formula (wff) correct?
\[ \neg A \to (A \to B) \]
**Proof:**
1. \( \neg A \to (\neg A \lor B) \)
2. \( \neg A \to (A \to B) \)
QED
---
**Answer Options:**
- ○ True
- ○ False
- ○ No idea
- ○ Where am I?
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