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, ?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 87E
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff43fe492-0086-4aac-90eb-2b796e708e5e%2F80b8a58f-8540-4797-9ae8-ff99bf44e066%2Fsko973p_processed.png&w=3840&q=75)
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff43fe492-0086-4aac-90eb-2b796e708e5e%2F80b8a58f-8540-4797-9ae8-ff99bf44e066%2F5r4t788_processed.png&w=3840&q=75)
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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