# 9.4.3 Yet more proof exercises

HW for Weds.                                     For each of these, what follows?  and by what rule ?

1. If Joe does proofs, he uses the rules to draw inferences.  Joe does do proofs.  Therefore _______

2. Either Joe uses the rules to draw inferences or else he can’t do proofs.  But he can do proofs. So _____

3. If Joe doesn’t use the rules, he can’t do proofs. But he can do proofs, so____________

4. If Joe can use DM, he can use IMP. If he can use IMP, he can use TRAN. So __________________

5. Joe can do proofs. Jane can do proofs.  So  ________________________________

6. Joe and Jane can do proofs. So   ___________________.

7. If Joe can do proofs, he can draw inferences, and if Jane can do proofs, she can substitute equivalent expressions.  Either Joe or Jane can do proofs, so ____________________________________.

8. Neither Joe nor Jane can do proofs. So ___________________________

9.  Not both of them can do proofs, so ___________________________

10. It’s not the case that neither Joe nor Jane can do proofs, so  ___________________________

Click on these links to pull up some exercise sets that are in pdf format.

In the first set (numbered 5-10) the full proof solution is provided. For the exercise you need, copy the first lines and the conclusion to a sheet of paper, and get to work. Then you can look back to this page for help.

Natural Deduction Exercises

In the set called “V,” you get some practice with Rules of Equivalence. In # 1 and 2, for example, you will need to use AD but also IMP.  Think backwards from the conclusion by IMP to see what you need to AD.  Remember that with AD, you can add anything you want, whether it is a single or a compound, whether affirmative or negative.

Natural Deduction Exercises 2