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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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 ..., ...
