# Logic Math Quiz

Instructions (note: 5 points for this quiz are for submitting everything correctly as per these instructions)
A. If you can, print this quiz out, put solutions on it with pen or pencil, and submit a PDF. Please verify that your PDF
has all the pages, in order.
B. If you can’t do that, you may complete this on a PDF on a tablet. If you do this route, make sure that the file you
send back is correct. For example, changes made after the most recent ‘save’ may not appear in the file you actually
submit. Best to email the file to yourself first, and look it over to make sure it comes out OK before submitting. Again,
all pages, in order.
C. If neither A nor B is workable for you, you may just write out the solutions on plain paper and submit a PDF of those.
D. Regardless of whether you go with A, B or C, please double check your PDF before AND AFTER you submit it. Make
sure it has all pages, they are right-side-up, and all the markings you intend to be there are actually there. After you
submit the PDF, click on the link for your own submission to double-check that the file that Canvas has as your
submission is correct. See the image to see what you will click on do download your own submission:
E. For multiple choice questions, the graders will only assess the letter answer(s) you put down, so showing your work
is not required. Though doing the work will of course help you get the right answer. And if you get an answer wrong,
any work you show will help us explain to you (in office hours) where you went wrong.
F. For non-multiple choice questions, showing as much relevant work as possible is recommended. First, because
NOT correct, the work you show, if it is sensible and appears to manifest understanding of the material, can be the
basis for partial credit.
Philosophy 10 Quiz 3 Page 2 of 4
Name: _______________________ Section: _______ Date:___________
1. [10] In all of the following, lines 1 and 2 are premises. In which of the following is line 3 correctly derived
as specified by the stated justification? (There may be more than 1 correct answer.)
[ ] A
1. P
2. Q ⊃ ~P
3. ~Q 1, 2 MT
[ ] B
1. J ⊃ ~K
2. ~K
3. ~J 1, 2 MT
[ ] C
1. M ⊃ N
2. ~M
3. ~N 1, 2 MP
[ ] D.
1. A v C
2. D
3. (A v D) v D 2 DI
[ ] E.
1. (S v W) v X
2. ~X
3. S v W 1, 2 DS
2. [5] According to the syllabus, in which of the following conditions would the instructor be willing to adjust a
student’s final grade after it has been assigned?
[ ] A. If an error has been made adding points or recording scores
[ ] B. If the student’s assigned grade jeopardizes the student’s good academic standing
[ ] C. If the student agrees to have all their tests re-graded at the end of the quarter
[ ] D. All of the above
3. [10] Fill in justifications.
1. W ⊃ (G v L)
2. ~N v W
3. ~L • N / ∴ G
4. N ________
5. W ________
6. G v L ________
7. ~L ________
8. G ________
4. [10] Fill in the derived statements.
1. ~H ⊃ ~(L • B)
2. B
3. B ⊃ (L • ~J) / ∴ J v H
4. ________ 2, 3 MP
5. ________ 4 simp
6. ________ 2, 5 conj
7. ________ 1, 6 MT
8. ________ 7 DI
Philosophy 10 Quiz 3 Page 3 of 4
For Problems 5 and 6, do the indicated proof using only inference rules from Chapter 3 (not conditional
proof or any rules from Chapter 4, or indirect proof).
5. [15]
1. X • ~Z
2. ~Z ⊃ Y / ∴ X • Y
6. [15]
1. M ⊃ ~Q
2. Q • ~H
3. M v H / ∴ D v H
For problems 7 and 8, use only inference rules, and you may also use conditional proof (that is, any
methods from Chapter 3).
7. [15]
1. P ⊃ ~K
2. K v Q / ∴ P ⊃ Q
8. [15]
1. B ⊃ ~(A ⊃ C)
2. ~C ⊃ ~A / ∴ D v ~B
Philosophy 10 Quiz 3 Page 4 of 4
Optional Question (Use inference rules and conditional proof, but no replacement rules or indirect
proof.)
Hint: One way to do this uses one or more conditional proofs and dilemma. Note that commutation is a
replacement rule, so don’t use that!
1. E ⊃ ~E
2. D ⊃ ~D
3. ~D ⊃ E
4. E v D

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