Make a folder, place all your saved ndp files in the folder, zip it, and submit the zipped-file to K-State Online.
Please do your own work --- no file sharing is allowed. Whatever you submit must be stored in your brain as well as in your computer files.
Please use the checker to prove these sequents.
The proofs are straightforward, even easy, if you consciously apply the tactics
for the rules, ^i, ve, and ->i.
1.
(p ^ q), r |− (p ^ r) ^ (s v q)
(Hint: use rules for ^ and v. No boxes appear in the proof.)
2.
p -> q, (p ^ q) -> r, p |− r ^ q
(Use ->e and the rules for ^.)
3.
p v (q ^ r) |− (p v q) ^ (p v r)
(Start by applying the tactic for ve.)
4.
p -> (q -> r) |− (p ^ q) -> r
(What tactic works best to prove a goal with an -> in it?)
5.
p -> (q ^ r) |− (p -> q) ^ (p -> r)
(The proof requires two uses of
->i.)