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


P ∨ Q =

M ⊃ ¬ Q

M =conjunction




(P V Q) ∧ ¬ Q

P ⊃ R =hypothetical syllogism

R ⊃ S =hypothetical syllogism



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.

closed as unclear what you're asking by Conifold, Frank Hubeny, Mauro ALLEGRANZA, Jishin Noben, virmaior Mar 15 at 19:20

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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 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 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 at 22:18
  • Would this be a good first start with modus ponens? – Drew McElwain Mar 6 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 at 22:20

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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