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

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter2: Parallel Lines
Section2.CT: Test
Problem 3CT: To prove a theorem of the form "If P, then Q" by the indirect method, the first line of the proof...
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Consider this proof (indentations have been removed) for a F-L Axiom system:
1.А — В
P
2.A
P[for A → B]
3.А — (В — А)
Ахiom 1
4.B → A
2, 3, MP
2 —4, СР
6.(А — В) — (В— А) 1,5, СР
5.А — (В — А)
-
Which is most accurate?
Correct proof
Incorrect at line 2
Incorrect at line 5
Incorrect at line 6
Transcribed Image Text:Consider this proof (indentations have been removed) for a F-L Axiom system: 1.А — В P 2.A P[for A → B] 3.А — (В — А) Ахiom 1 4.B → A 2, 3, MP 2 —4, СР 6.(А — В) — (В— А) 1,5, СР 5.А — (В — А) - Which is most accurate? Correct proof Incorrect at line 2 Incorrect at line 5 Incorrect at line 6
Consider the Hilbert-Ackerman (H-A) Axioms:
1.A VA — А
2.А — A V В
3.A VВ — ВVA
→ BVA
4.(A → B) → (C V A → C v B)
→ (C V A → C V B)
Proof rules: MP and A → B = ¬A v B
Is the following proof of the given wff correct?
-A (А — В)
Proof:
1.¬A → (¬A v B)
2.-А — (А — В)
QED
True
False
O No idea
Where am I?
Transcribed Image Text:Consider the Hilbert-Ackerman (H-A) Axioms: 1.A VA — А 2.А — A V В 3.A VВ — ВVA → BVA 4.(A → B) → (C V A → C v B) → (C V A → C V B) Proof rules: MP and A → B = ¬A v B Is the following proof of the given wff correct? -A (А — В) Proof: 1.¬A → (¬A v B) 2.-А — (А — В) QED True False O No idea Where am I?
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