Practice Exam #3
General Instructions: This exam has nine parts. Be sure to complete each part. Read the instructions completely before attempting to answer specific questions. All answers go in a blue book with your name on it.
Part I True or False? (10 points)
1. According to the Traditional Square of Opposition, the inference from a Universal Affirmative to a particular affirmative categorical sentence is a valid inference.
2. According to the Traditional Square of Opposition, if an A categorical sentence is true, then the corresponding E categorical sentence must be false.
3. (∃x)(Fx ⊃ Ga) is a conditional.
4. (x)~(Sx & Rx) is equivalent to ~(∃x)(Sx & Rx).
5. (x)((Fx & Gx) ⊃ Hx) has a complex subject.
Part II Classification and Translation (10 points)
First, classify each of the following sentences as either:
(a) Singular proposition
(b) simple quantified proposition
(c) Categorical proposition
(d) negation of a quantified proposition
(e) truth‑functional compounds
Second, translate each sentence into QL.
1. It is not true that Ignat is friendly.
2. The White House is a lovely building.
3. Residents of Wisconsin eat a lot of cheese.
4. If you like logic, then you are crazy.
5. Fritz is small and shy, but all rodents are.
Part III Categorical Sentences (2 points each, 10 points total)
For each of the following sentences, classify as either an A,I, E or O type categorical sentence and translate into QL.
1. Each house in the valley is lovely.
2. Some human acts aren't determined.
3. None of the clerks was shot.
4. Philosophers never lie.
5. The only good logician is a bald logician.
Part IV Syllogisms (10 points)
Test one of the following syllogisms for validity using the Venn Diagram method and state the mood and figure of each syllogism.
1. All logicians are smart
Some smart persons are not careful.
Some persons who are careful are not logicians.
2. No square things are apples.
No square things are tasty.
No tasty things are apples.
Part V Syllogisms – Truth Trees (10 points) Test one of the following syllogisms for validity using the numbered Truth-Tree method.
1. Some
Students are fickle.
No philosophers are fickle.
No philosophers are students.
2. No
rugby players are skiers.
Some skiers are not tough.
All rugby players are tough.
Part VI: Syllogisms – Rules for Valid Syllogisms (10 points each) Test one of the following syllogisms for validity using the Rules for Valid Syllogisms method. (10 points)
Part VII: Traditional and Revised Squares of Opposition (10 points)
Describe one relation among categorical propositions posited
by the traditional square of opposition but not by the revised square. Explain
why the traditional square is incorrect on this matter.
Part VIII Truth Trees for QL (10 points total) Test two of the following arguments for validity using the PL Truth Tree Method.
1. ~(∃x)(Sx & ~Px), Sa /// Pa
2. (x)Rx ⊃ (∃x)~Sx, (x)Sx /// (∃x)~Rx