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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
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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**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
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?
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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