Symbolic Logic Rules of Implication

 

For each line (other than the premises) in the following proofs, state the line or lines which it follows and the valid argument form (MP, MT, DS, or HS) used to obtain it.

The boxes on the left are for the applicable lines and the boxes on the right are for the applicable rules. 

(1)  

1. A ⊃ B         Premise

2. A ∨ C         Premise

3. ~B               Premise

4. ~A                  

5. C         

(2)

 

1. A ∨ (H ∙ K)          Premise

2. A ⊃ (B ∨ C)         Premise

3. ~ (B ∨ C)              Premise

4. ~A                              

5. (H ∙ K)                      

(3)

 

1. ~R                         Premise

2. ~S ⊃ T                 Premise

3. (A ⊃ B) ⊃ ~S     Premise

4. ~R ⊃ (A ⊃ B)    Premise

5. ~R ⊃ ~S                 

6. ~R ⊃ T                    

7. T                             

(4)

  For each line (other than the premises) in the following proofs, state the line or lines which it follows and the valid argument form (MP, MT, DS, HS, Simp, Conj, Com, Add, CD) used to obtain it.

The boxes on the left are for the applicable lines and the boxes on the right are for the applicable rules. 

1. A ⊃ B                  Premise

2. A ∙ ~D                 Premise

3. B ⊃ C                   Premise

4. A                               

5. A ⊃ C                      

6. C                               

7. ~D ∙ A                     

8. ~D                            

9. C ∙ ~D                    

(5)

 

1. C                                Premise

2. A ⊃ B                        Premise

3. C ⊃ D                       Premise

4. D ⊃ E                       Premise

5. C ⊃ E                          

6. C ∨ A                          

7. (C ⊃ E) ∙ (A ⊃ B)     

8. E ∨ B                            

(6)

 

Use the first eight rules of inference to derive the conclusion of the following symbolized argument (you can use another sheet of paper). If you can't access the logical operation signs, just write "dot," "wedge", "horseshoe" or "triple bar" wherever applicable.

1. ( W ∙ X ) ⊃ ( Q ∨ R )
2. ( S ∨ F ) ⊃ ( Q ∨ W )
3. ( S ∨ G ) ⊃ ( ~ Q ⊃ X )
4. Q ∨ S
5. ~ Q ∙ H                                  /    R