Phi 270 F05 test 3
F05 test 3 topics
The following are the topics to be covered. The proportion of the test covering each will approximate the proportion of the classes so far that have been devoted to that topic. Your homework and the collection of old tests will provide specific examples of the kinds of questions I might ask.
Analysis. Two sorts of questions are possible here corresponding to the sorts of analyses you have done in chs. 5 and 6: (i) analysis by truth-functional connnectives alone, with atomic sentences as the ultimate components (the emphasis will, of course, be on conditionals—i.e., on the symbolic representation of if, only if, and unless) and (ii) analysis using not only truth-functional connnectives but also predicates, individual terms, and functors.
Derivations. Be able to construct derivations to show that entailments hold and to show that they fail. I may tell you in advance whether an entailment holds or leave it to you to check that using derivations. There may be some derivations where detachment and attachment rules may be used and where they will shorten the proof. But there will be others where you must rely on other rules, either because detachment and attachment rules do not apply or because I tell you not to use them. In particular, be ready to use the rule RC (Rejecting a Conditional) from ch. 5.
Remember that, if a derivation involves predicates and functors, presenting a counterexample will require the description of a structure and not merely an assignment of truth values. You will be allowed to use either tables or diagrams to describe structures.
F05 test 3 questions
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Analyze the sentences below in as much detail as possible using only connectives; that is, the unanalyzed components should all be sentences (rather than individual terms, predicates, or functors). Present the result in both symbolic and English notation. Be sure that the unanalyzed components of your answer are complete and independent sentences; also try to respect any grouping in the English. |
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| 1. |
If the part was fixed, it broke again.
answer |
| 2. |
Unless Tom was early, he got in only if he paid extra.
answer |
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Use derivations to check whether each of the entailments below holds. You may use detachment and attachment rules. If an entailment fails, present a counterexample that divides an open gap. |
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| 3. |
A → (B → C), C → D ⊨ B → (A → D)
answer |
| 4. |
(C ∧ A) → B ⊨ (A ∧ B) → C
answer |
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Analyze the sentence below in as much detail as possible, giving a key to your abbreviations of unanalyzed expressions. In this case you should identify components that are individual terms, predicates, or functors; however, you do not need to present the result in English notation (i.e., symbolic notation is enough). (Be sure that the unanalyzed components of your answer are independent—in particular, that none contains a pronoun whose antecedent is in another—and be sure also that the individual terms you identify really are individual terms rather than general terms or quantifier phrases.) |
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| 5. |
Either Fred is the manager or he owns the business.
answer |
| 6. |
Sam received a recall notice from the manufacturer of his car.
answer |
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Use a derivation to show that the entailment below holds. You may use detachment and attachment rules. (Be sure to indicate the alias sets whenever an equation is added to the resources.) |
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| 7. |
Rb(fa), fb = gc, c = fb, d = gc ⊨ c = d ∧ (a = b → Ra(gd))
answer |
F05 test 3 answers
| 1. |
If the part was fixed, it broke again the part was fixed → the part broke again
F → B
B: the part broke again; F: the part was fixed |
| 3. |
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| 5. |
Either Fred is the manager or he owns the business Fred is the manager ∨ Fred owns the business Fred = the manager ∨ [ _ owns _ ] Fred the business f = m ∨ Ofb O: [ _ owns _ ]; b: the business; f: Fred; m: the manager |
| 6. |
Sam received a recall notice from the manufacturer of his car Sam received a recall notice from the manufacturer of his car [ _ received a recall notice from _ ] Sam the manufacturer of Sam’s car R s (the manufacturer of Sam’s car) R s ([the manufacturer of _ )] Sam’s car) R s (m (Sam’s car)) R s (m ([ _’s car] Sam)) Rs(m(cs)) R: [ _ received a recall notice from _ ]; c: [ _’s car]; m: [the manufacturer of _ ]; s: Sam |
| 7. |
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