Philosophy homework

Submission Instructions: You may either complete this module using Canvas text entry (do your best with formatting and logical operators) or you may copy and paste it into your word processing software, and upload the completed assignment as either a MSWord document or Adobe document. You may also complete it by hand, take photos, and upload them.

Proofs are confusing at first, so be sure you've watched the VLecture and read chapter 8.1.

Directions: Complete the following proofs below using any of the 8 implicational rules (as found in the inside cover of the text as well as chapter 8, section 1.) . Feel free to use the following key for copying and pasting the logical operators and conclusion symbol.

Negation: ~

Conjunction: ⦁

Disjunction:⌵

Conditional: →

Biconditional: ↔ 

Conclusion: ∴

(#1)

1. (A ⦁ B) ⦁ (C ⦁ D)

∴ A

 

 

 

 

 

(#2)

1. P

∴ P ⌵ Q

 

 

 

 

 

 

(#3)

1. (R → S) ⦁ (S → R)

∴ R → R

 

 

 

 

 

 

 

(#4)

1. (A ⌵ B) ⌵ C

2. ~C ⦁ ~B

∴ A

 

 

 

 

 

(#5)

1. (M → N) ⌵ ~O

2. P → O

3. ~(M → N)

∴ ~P

 

 

 

 

 

 

(#6)

1. P → R

2. R → S

3. ~S

∴ ~P

 

 

 

 

 

(#7)

1. (A ⌵ B) ⦁ C

2. C → ~A

∴ B

 

 

 

 

 

 

(#8)

1. (A ↔ B) → C

2. X → D

3. X ⦁ (A ↔ B)

∴ C ⦁ D

 

 

 

 

 

 

(#9)

1. (P → R) ⦁ (S → T)

2. P ⌵ S

3. ~T

∴ R