We will review several of these questions at classtime on October 23, so please bring a copy of your work to class.
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 prove these sequents:
1.
p ∧ q |− (p ∨ s) ∧ (r ∨ q)
(Use the ∧i, ∧e, and ∨i rules.)
2.
(p ∧ q) ∨ r |− (p ∨ r) ∧ (q ∨ r)
(The proof is a cases analysis, finishing with ∨e.
Use ∨i, ∧i, and ∧e within the two cases.)
3.
p —> r, q —> s |− (p ∧ q) —> (r ∧ s)
(Use ∧i, ∧e, —>e.)
4.
p —> r, q —> s |− (p ∨ q) —> (r ∨ s)
(This proof requires nested subproofs. One finishes with —>i;
the other finishes with ∨e.)