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Consider the following proof of that IS supposed to prove the tautology: (A v B → C^ D) → (B → D) Proof: 1. AVВ — СлD P 2. ¬(B → D) P for IP 3. B^ ¬D 2 4. B 3, ?

Consider the following proof of that IS supposed to prove the tautology: (A v B → C^ D) → (B → D) Proof: 1. AVВ — СлD P 2. ¬(B → D) P for IP 3. B^ ¬D 2 4. B 3, ?

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.3: The Field Of Quotients Of An Integral Domain
Problem 6E
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Consider the following proof of that is supposed to prove the tautology: (AVВ — СЛD) — (В — D) Proof: 1. AVВ — СлD P 2. -(В — D) P for IP 3. B^ ¬D 2 4. В 3, ? 5. A V B 4, ? 6. СЛD 1,5, ? 7. ¬D 3, ? 8. D 6, ? 9. DA¬D 7,8, ? 10. False 9, Contr QED 1,2, 10, IP The above proof is correct. However in lines 4 -- 9 we have not indicated the Proof Rule being used (indicated by a `?'). Which of the following choices gives the correct sequence of Proof Rules for these lines? Add, Add, Conj, DN, Contr, Conj Simp, Add, MP, Simp, Simp, Conj Simp, Simp, Add, Simp, DN, Contr Add, Simp, Simp, Simp, Simp, Contr
Transcribed Image Text:Consider the following proof of that is supposed to prove the tautology: (AVВ — СЛD) — (В — D) Proof: 1. AVВ — СлD P 2. -(В — D) P for IP 3. B^ ¬D 2 4. В 3, ? 5. A V B 4, ? 6. СЛD 1,5, ? 7. ¬D 3, ? 8. D 6, ? 9. DA¬D 7,8, ? 10. False 9, Contr QED 1,2, 10, IP The above proof is correct. However in lines 4 -- 9 we have not indicated the Proof Rule being used (indicated by a `?'). Which of the following choices gives the correct sequence of Proof Rules for these lines? Add, Add, Conj, DN, Contr, Conj Simp, Add, MP, Simp, Simp, Conj Simp, Simp, Add, Simp, DN, Contr Add, Simp, Simp, Simp, Simp, Contr
Consider the following proof of the tautology: (А — С) - (А лВ ъ С) Proof: 1. A → C 2. АЛВ 3. A 4. C 5. АЛВ — С QED This proof is an example of applying: Neither IP nor CP Rules Both CP and IP Rules IP Rule CP Rule
Transcribed Image Text:Consider the following proof of the tautology: (А — С) - (А лВ ъ С) Proof: 1. A → C 2. АЛВ 3. A 4. C 5. АЛВ — С QED This proof is an example of applying: Neither IP nor CP Rules Both CP and IP Rules IP Rule CP Rule
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