1

Prove the following symbolized arguments applying the appropriate rules of inference:

1)

P ∨ Q =

M ⊃ ¬ Q

M =conjunction

Therefore

P

2)

(P V Q) ∧ ¬ Q

P ⊃ R =hypothetical syllogism

R ⊃ S =hypothetical syllogism

Therefore

S

I have watched countless videos on how to do these questions and this is all I was given as to complete the questions. I'm unsure if i'm even doing it correctly if im not just finding the right rules for each line.

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  • I am not sure what you are trying to do. Which lines are assumptions? You might try using the this proof checker to help with these problems: proofs.openlogicproject.org – Frank Hubeny Mar 6 '19 at 22:10
  • Review your list of rules of inference and find the suitable one to be used with M and M ⊃ ¬ Q, and so on. – Mauro ALLEGRANZA Mar 6 '19 at 22:16
  • So, the conclusion would be 1=p and 2=s and everything above that is assumptions. I'm unfamiliar with this concept so sorry if it's confusing. – Drew McElwain Mar 6 '19 at 22:18
  • Would this be a good first start with modus ponens? – Drew McElwain Mar 6 '19 at 22:20
  • If this is a HW question you need to explain your efforts to solve it for us to help. And regardless, please reformat it into a more readable form, and add some explanatory text. – Conifold Mar 6 '19 at 22:20
2

You appear to be asked to prove the conclusion from the premises using certain rules of inference.

I'll do you a favour and list the rules you need, but leave it to you to replace the elipsis.

1.|  P ∨ Q        premise
2.|  M ⊃ ¬ Q      premise
3.|_ M            premise
4.|  ...       by modus ponens ..., ...    
5.|  P            disjunctive syllogism ..., ...

.

1.|   (P V Q) ∧ ¬ Q    premise 
2.|   P ⊃ R            premise
3.|_  R ⊃ S            premise
4.|   ...           by hypothetical syllogism ..., ... 
5.|   ...              simplification ...
6.|   ...              simplification ...
7.|   ...              disjunctive syllogism ..., ...                 
8.|   S                modus ponens ..., ...
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