Exercises for Chapter 5, Part 1

10 points. Due Saturday 3 March, 10pm
For each of the questions that follow, type your answers in the CIS301 Natural Deduction Proof Checker. Use the Checker to save each answer. (E.g., for Question 1, save the file as Q1 --- the Checker creates the file, Q1.ndp.)

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:

1.
(p ^ q), r |- (p ^ r) ^ (s v q)
(Hint: use some of the rules for ^ and v.)

2.
p v (q ^ r) |- (p v q) ^ (p v r)
(Hint: The proof is a cases analysis, finishing with ve. The other rules for ^ and v are also needed.)

3.
p -> q, (p ^ q) -> r, p |- r ^ q
(Use ->e and the rules for ^.)

4.
p -> (q -> r) |- (p ^ q) -> r
(Use rules for -> and ^.)

5.
p -> r, q -> s |- (p v q) -> (r v s)
(There are nested boxes in the proof, because both ve as well as ->i are required.)