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(1) 1. B ⊃ (∼ C ⋅ ∼ D) 2. C ∨ D 3. B /∴ ∼ D ⊃ C    (3) 1. A ⋅ ∼ B 2. B ⊃ A 3. A ⊃ B /∴ B    (5) 1. A ⊃ (B ∨ C) 2. ∼ (∼ A ∨ C) 3. ∼ B /∴ C

(1) 1. B ⊃ (∼ C ⋅ ∼ D) 2. C ∨ D 3. B /∴ ∼ D ⊃ C    (3) 1. A ⋅ ∼ B 2. B ⊃ A 3. A ⊃ B /∴ B    (5) 1. A ⊃ (B ∨ C) 2. ∼ (∼ A ∨ C) 3. ∼ B /∴ C

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Exercise 5-7 A. Prove that the following arguments all have inconsistent premises. please help with numbers 1-9

(1) 1. B ⊃ (∼ C ⋅ ∼ D)

2. C ∨ D

3. B /∴ ∼ D ⊃ C 

 

(3) 1. A ⋅ ∼ B

2. B ⊃ A

3. A ⊃ B /∴ B 

 

(5) 1. A ⊃ (B ∨ C)

2. ∼ (∼ A ∨ C)

3. ∼ B /∴ C 

 

(7) 1. K ⊃ (L ⊃ M)

2. N ∨ K

3. ∼ (∼ L ∨ M)

4. ∼ N /∴ K ⊃ (∼ M ∨ L)

 

(9) 1. A ⊃ (C ⊃ D)

2. ∼ A ⊃ (D ⊃ C)

3. (A ∨ ∼ A) ⊃ ∼ D

4. (A ⋅ D) ∨ (∼ A ⋅ ∼ D)

5. (C ⋅ D) ∨ (∼ C ⋅ ∼ D)

6. A /∴ D

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