Logic Math Quiz

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all pages, in order.
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F. For non-multiple choice questions, showing as much relevant work as possible is recommended. First, because
working a problem out completely and carefully will help you get the correct answer. And also second, if your answer is
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.
Put Multiple Choice Answers Here
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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