| Phi 270 Fall 2013 |
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Phi 270 F98 test 3
F98 test 3 questions
(Questions 1-6 are from quiz 3 and 7-10 are from quiz 4 out of 6 quizzes—these two quizzes addressed the part of the course your test is designed to cover.)
| Analyze the sentences below in as much detail as possible without going below the level of sentences (i.e., without recognizing individual terms and predicates). Be sure that the unanalyzed components of your answer are complete and independent sentences and that you respect any grouping in the English. You may use right-to-left arrows to reflect English word order but you should then also restate your symbolic analysis with arrows running left to right and, in any case, you should restate it using English notation. | ||
| 1. |
If our message got there, they should be on their way
answer |
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| 2. |
Unless we make reservations, we’ll get a table only if it is a slow night
answer |
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| 3. | Check the following for validity using derivations; you may use attachment rules and detachment rules. If the derivation fails, confirm a counterexample that lurks in an open gap. |
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A → (B → (C ∨ D))
answer
¬ C → (A → ¬ B) |
| 4. | [This question was on a topic not covered this year] |
| 5. |
Analyze the sentence below in as much detail as possible, continuing the analysis when there are no more connectives by identifying predicates, functors, and individual terms. Be sure that the unanalyzed expressions in your answer are independent and that you respect any grouping in the English. (You need not state the result in English notation.)
If Sam is the winner of the trip, then the winner of the grand prize presented it to him
answer
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| 6. | Give two different expansions (using predicate abstracts) of the sentence below as a one-place predicate applied to a term: |
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Pb ∧ Rab
answer
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| 7. | Draw a diagram which presents the same interpretation as the following tables: | ||||||||||||||||||||||||||||||||||||||||||||
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| 8. |
Describe a structure (i.e., an assignment of extensions to the non-logical vocabulary) which makes the following sentences all true. (You may present the structure either using tables or using diagrams.)
fa = b, b = c, Pb, ¬ Pa, Ra(fa), R(fb)(fc), ¬ Rbc
answer
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| Check each of the arguments below for validity using derivations. You need not present counterexamples to gaps that reach dead ends. | ||
| 9. |
fa = c
answer
Rbc a = b → Ra(fa) |
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| 10. |
Rab ∨ Rcb
answer
a = b ∧ gb = gc Rbc → Rcb |
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F98 test 3 answers
| 1. |
If our message got there, they should be on their way our message got there → they should be on their way
M → W
M: our message got there; W: they should be on their way |
| 4. | [This question was on a topic not covered this year] |
| 5. |
If Sam is the winner of the trip, then the winner of the grand prize presented it to him Sam is the winner of the trip → the winner of the grand prize presented the trip to Sam s = the winner of the trip → [ _ presented _ to _ ]the winner of the grand prize the trip Sam s = [the winner of _ ] the trip → P(the winner of the grand prize)ts s = nt → P([the winner of _ ] the grand prize)ts s = nt → P(ng)ts P: [ _ presented _ to _ ]; g: the grand prize; n: [the winner of _ ]; s: Sam; t: the trip |
| 6. |
The following are the possibilities; in the last, τ may be any term:
[Pb ∧ Rxb]xa, [Px ∧ Rab]xb, [Pb ∧ Rax]xb, [Px ∧ Rax]xb, [Pb ∧ Rab]xτ
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| 7. |
| 8. |
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(The diagram above provides a complete answer, and so do the tables to its left. The tables below show a way of arriving at these answers.) |
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| 9. |
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| 10. |
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