Rules of Inference III

 

Instructions: Print out this page. For each of the following derivations, complete the justification by providing the rule of inference and line numbers. Answers are here.

 

 

A.

1. (A v B) ⊃ (C & D) premise
2. (~A & B) premise
3. (C & D) ⊃ (L v M) premise
4. (A v B)  ⊃ (L v M)    
5. ~A     
6. B    
7. (A v B)    
8. (L v M)    

B.

1. (A ⊃ B) ⊃ ~C) premise
2. ((A ⊃ B) v B) premise
3. (B ⊃ E) premise
4. ~B premise
5. (~C v E)    
6. (A ⊃ B)    
7. ~B v E    
8. (~B v E) & (B ⊃ E)    
9. ~B & (~C v E)    

C.

1. (E ⊃ ~F) & (R ⊃ C) premise
2. E & (~C ⊃ (L & ~P)) premise
3. (R & S) & (X ⊃ F) premise
4. E    
5. (E ⊃ ~F)    
6. (R ⊃ C)    
7.  (~C ⊃ (L & ~P))    
8. R & S    
9. (X ⊃ F)    
10. ~F    
11. ~X