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Introduction to Logic: Reading Exercises
Essay Instructions:
Complete the exercises in the attached document, “Reading Exercises.” These exercises are in the textbook, refer to your text should you have questions or need further examples.
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Introduction to Logic: Reading Exercises
6.1 INSTRUCTIONS
Rewrite each of the following syllogisms in standard form, and name its mood and figure. (Procedure: first, identify the conclusion; second, note its predicate term, which is the major term of the syllogism; third, identify the major premise, which is the premise containing the major term; fourth, verify that the other premise is the minor premise by checking to see that it contains the minor term, which is the subject term of the conclusion; fifth, rewrite the argument in standard form—major premise first, minor premise second, conclusion last; sixth, name the mood and figure of the syllogism.)
Example Problem
No nuclear-powered submarines are commercial vessels, so no warships are commercial vessels, because all nuclear-powered submarines are warships.
Example Solution
Step 1.
The conclusion is “No warships are commercial vessels.”
Step 2.
“Commercial vessels” is the predicate term of this conclusion and is therefore the major term of the syllogism.
Step 3.
The major premise, the premise that contains this term, is “No nuclear-powered submarines are commercial vessels.”
Step 4.
The remaining premise, “All nuclear-powered submarines are warships,” is indeed the minor premise, because it does contain the subject term of the conclusion, “warships.”
Step 5.
In standard form this syllogism is written thus:
No nuclear-powered submarines are commercial vessels.All nuclear-powered submarines are warships.Therefore no warships are commercial vessels.
Step 6.
The three propositions in this syllogism are, in order, E, A, and E. The middle term, “nuclear-powered submarines,” is the subject term of both premises, so the syllogism is in the third figure. The mood and figure of the syllogism therefore are EAE-3.
PROBLEMS
2. Some evergreens are objects of worship, because all fir trees are evergreens, and some objects of worship are for trees.
Step 1: The conclusion is “All fir trees are evergreen”
Step 2: “Objects of worship” is the predicate term thus, the major syllogism.
Step 3: “some objects of worship are evergreen” is the major premise
Step 4: “Therefore, some evergreens are objects of worship” is the minor premise
Step 5: “All fir trees are evergreens, some evergreens are objects of worship, and some objects of worship are evergreens” is the standard syllogism.
Step 6: IAI-4
3. All artificial satellites are important scientific achievements; therefore some important scientific achievements are not U.S. inventions, in as much as some artificial satellites are not U.S. inventions.
Step 1: Some important scientific achievements are not U.S. inventions is the conclusion thus the predicament term of the conclusion is “ scientific achievement”
Step 2:The major term that contain the major premise is “ some scientific achievement are not U.S. inventions”
Step 3: the minor premise is that “some artificial satellites are not U.S. inventions” as it contains the subject term of the conclusion “ artificial satellites”
Step 4: all artificial satellites are important scientific achievements
Step 5: Thus, the syllogism is written;
Some artificial satellites are not U.S. inventions
All artificial satellites are important scientific achievements
Therefore, important scientific achievements are not U.S. inventions.
Step 6: OAO3
4. No television stars are certified public accountants, but all certified public accountants are people of good business sense; it follows that no television stars are people of good business sense.
Step 1: All certified public accountants are people of good business sense
Step 2: People of good business sense
Step 3: No television stars are certified, public accountants
Step 4: No television stars are people of good business sense.
Step 5: All certified public accountants are people of good business sense. No television stars are certified, public accountants. No television stars are not people of good business sense.
Step 6: AEE-1
5. Some conservatives are not advocates of high tariff rates, because all advocates of high tariff rates are Republicans, and some Republicans are not conservatives.
Step 1: “Some conservatives are not advocates of high tariff rates” is the conclusion
Step 2: “Advocates of high tariff rates” predicate the term of the conclusion thus, the major term.
Step 3: “All advocates of high tariff rates are Republicans” major premise
Step 4: “Some Republicans are not conservatives” minor premises
Step 5: All advocates of high tariff rates are Republican, some Republicans are not conservatives, some conservatives are not advocates of high tariff rates.
Step 6: AOO-6
6. All CD players are delicate mechanisms, but no delicate mechanisms are suitable toys for children; consequently, no CD players are suitable toys for children.
Step 1: No delicate mechanisms are suitable toys for children
Step 2: Suitable toys for children
Step 3: All CD players are delicate mechanisms
Step 4: No CD players are suitable toys for children
Step 5: All CD players are delicate mechanisms, no CD players are suitable for toys for children, and therefore no delicate mechanisms are suitable toys for children.
Step 6: EAE-1
7. All juvenile delinquents are maladjusted individuals, and some juvenile delinquents are products of broken homes; hence some maladjusted individuals are products of broken homes.
Step 1: Some maladjusted individuals are products of broken homes
Step 2: Products of broken homes
Step 3: Some juvenile delinquents are products of broken homes
Step 4: All juvenile delinquents are maladjusted individuals
Step 5: Some juvenile delinquents are products of broken homes, all juvenile delinquents are maladjusted individuals, therefore some maladjusted individuals are products of broken homes.
Step 6: IAI-3
8. No stubborn individuals who never admit a mistake are good teachers, so, because some well-informed people are stubborn individuals who never admit a mistake, some good teachers are not well-informed people.
Step 1: Some good teachers are not well-informed people. Step 2: well-informed people Step 3: Some well-informed people are stubborn individuals who never admit a mistake Step 4: No stubborn individuals who never admit a mistake are good teachers
Step 5: Some well-informed people are stubborn individuals who never admit a mistake, no stubborn individuals who never admit a mistake are good teachers, hence some good teachers are not well-informed people.
Step 6: IEO-4
9. All proteins are organic compounds, hence all enzymes are proteins, as all enzymes are orga...
6.1 INSTRUCTIONS
Rewrite each of the following syllogisms in standard form, and name its mood and figure. (Procedure: first, identify the conclusion; second, note its predicate term, which is the major term of the syllogism; third, identify the major premise, which is the premise containing the major term; fourth, verify that the other premise is the minor premise by checking to see that it contains the minor term, which is the subject term of the conclusion; fifth, rewrite the argument in standard form—major premise first, minor premise second, conclusion last; sixth, name the mood and figure of the syllogism.)
Example Problem
No nuclear-powered submarines are commercial vessels, so no warships are commercial vessels, because all nuclear-powered submarines are warships.
Example Solution
Step 1.
The conclusion is “No warships are commercial vessels.”
Step 2.
“Commercial vessels” is the predicate term of this conclusion and is therefore the major term of the syllogism.
Step 3.
The major premise, the premise that contains this term, is “No nuclear-powered submarines are commercial vessels.”
Step 4.
The remaining premise, “All nuclear-powered submarines are warships,” is indeed the minor premise, because it does contain the subject term of the conclusion, “warships.”
Step 5.
In standard form this syllogism is written thus:
No nuclear-powered submarines are commercial vessels.All nuclear-powered submarines are warships.Therefore no warships are commercial vessels.
Step 6.
The three propositions in this syllogism are, in order, E, A, and E. The middle term, “nuclear-powered submarines,” is the subject term of both premises, so the syllogism is in the third figure. The mood and figure of the syllogism therefore are EAE-3.
PROBLEMS
2. Some evergreens are objects of worship, because all fir trees are evergreens, and some objects of worship are for trees.
Step 1: The conclusion is “All fir trees are evergreen”
Step 2: “Objects of worship” is the predicate term thus, the major syllogism.
Step 3: “some objects of worship are evergreen” is the major premise
Step 4: “Therefore, some evergreens are objects of worship” is the minor premise
Step 5: “All fir trees are evergreens, some evergreens are objects of worship, and some objects of worship are evergreens” is the standard syllogism.
Step 6: IAI-4
3. All artificial satellites are important scientific achievements; therefore some important scientific achievements are not U.S. inventions, in as much as some artificial satellites are not U.S. inventions.
Step 1: Some important scientific achievements are not U.S. inventions is the conclusion thus the predicament term of the conclusion is “ scientific achievement”
Step 2:The major term that contain the major premise is “ some scientific achievement are not U.S. inventions”
Step 3: the minor premise is that “some artificial satellites are not U.S. inventions” as it contains the subject term of the conclusion “ artificial satellites”
Step 4: all artificial satellites are important scientific achievements
Step 5: Thus, the syllogism is written;
Some artificial satellites are not U.S. inventions
All artificial satellites are important scientific achievements
Therefore, important scientific achievements are not U.S. inventions.
Step 6: OAO3
4. No television stars are certified public accountants, but all certified public accountants are people of good business sense; it follows that no television stars are people of good business sense.
Step 1: All certified public accountants are people of good business sense
Step 2: People of good business sense
Step 3: No television stars are certified, public accountants
Step 4: No television stars are people of good business sense.
Step 5: All certified public accountants are people of good business sense. No television stars are certified, public accountants. No television stars are not people of good business sense.
Step 6: AEE-1
5. Some conservatives are not advocates of high tariff rates, because all advocates of high tariff rates are Republicans, and some Republicans are not conservatives.
Step 1: “Some conservatives are not advocates of high tariff rates” is the conclusion
Step 2: “Advocates of high tariff rates” predicate the term of the conclusion thus, the major term.
Step 3: “All advocates of high tariff rates are Republicans” major premise
Step 4: “Some Republicans are not conservatives” minor premises
Step 5: All advocates of high tariff rates are Republican, some Republicans are not conservatives, some conservatives are not advocates of high tariff rates.
Step 6: AOO-6
6. All CD players are delicate mechanisms, but no delicate mechanisms are suitable toys for children; consequently, no CD players are suitable toys for children.
Step 1: No delicate mechanisms are suitable toys for children
Step 2: Suitable toys for children
Step 3: All CD players are delicate mechanisms
Step 4: No CD players are suitable toys for children
Step 5: All CD players are delicate mechanisms, no CD players are suitable for toys for children, and therefore no delicate mechanisms are suitable toys for children.
Step 6: EAE-1
7. All juvenile delinquents are maladjusted individuals, and some juvenile delinquents are products of broken homes; hence some maladjusted individuals are products of broken homes.
Step 1: Some maladjusted individuals are products of broken homes
Step 2: Products of broken homes
Step 3: Some juvenile delinquents are products of broken homes
Step 4: All juvenile delinquents are maladjusted individuals
Step 5: Some juvenile delinquents are products of broken homes, all juvenile delinquents are maladjusted individuals, therefore some maladjusted individuals are products of broken homes.
Step 6: IAI-3
8. No stubborn individuals who never admit a mistake are good teachers, so, because some well-informed people are stubborn individuals who never admit a mistake, some good teachers are not well-informed people.
Step 1: Some good teachers are not well-informed people. Step 2: well-informed people Step 3: Some well-informed people are stubborn individuals who never admit a mistake Step 4: No stubborn individuals who never admit a mistake are good teachers
Step 5: Some well-informed people are stubborn individuals who never admit a mistake, no stubborn individuals who never admit a mistake are good teachers, hence some good teachers are not well-informed people.
Step 6: IEO-4
9. All proteins are organic compounds, hence all enzymes are proteins, as all enzymes are orga...
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