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EXERCISE A INSTRUCTIONS
State the converses of the following propositions, and indicate which of them are equivalent to the given propositions:
PROBLEMS
1. No people who are considerate of others are reckless drivers who pay no attention to traffic regulations.
2. All graduates of West Point are commissioned officers in the U.S. Army.
3. Some European cars are overpriced and underpowered automobiles.
4. No reptiles are warm-blooded animals.
5. Some professional wrestlers are elderly persons who are incapable of doing an honest day’s work.
EXERCISE B INSTRUCTIONS
State the obverses of the following propositions:
PROBLEMS
1. Some college athletes are professionals.
2. No organic compounds are metals.
3. Some clergy are not abstainers.
4. No geniuses are conformists.
5. All objects suitable for boat anchors are objects that weigh at least fifteen pounds.
EXERCISE C INSTRUCTIONS
State the contrapositives of the following propositions and indicate which of them are equivalent to the given propositions.
PROBLEMS
1. All journalists are pessimists.
2. Some soldiers are not officers.
3. All scholars are nondegenerates.
4. All things weighing less than fifty pounds are objects not more than four feet high.
5. Some noncitizens are not nonresidents.
EXERCISE D INSTRUCTIONS
If “All socialists are pacifists” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?
PROBLEMS
1. Some nonpacifists are not nonsocialists.
2. No socialists are nonpacifists.
3. All nonsocialists are nonpacifists.
4. No nonpacifists are socialists.
5. No nonsocialists are nonpacifists.
6. All nonpacifists are nonsocialists.
7. No pacifists are nonsocialists.
8. Some socialists are not pacifists.
9. All pacifists are socialists.
10. Some nonpacifists are socialists.
EXERCISE E INSTRUCTIONS
If “No scientists are philosophers” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?
PROBLEMS
1. No nonphilosophers are scientists.
2. Some nonphilosophers are not nonscientists.
3. All nonscientists are nonphilosophers.
4. No scientists are nonphilosophers.
5. No nonscientists are nonphilosophers.
6. All philosophers are scientists.
7. Some nonphilosophers are scientists.
8. All nonphilosophers are nonscientists.
9. Some scientists are not philosophers. No philosophers are nonscientists.
EXERCISE F INSTRUCTIONS
If “Some saints were martyrs” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?
PROBLEMS
1. All saints were martyrs.
2. All saints were nonmartyrs.
3. Some martyrs were saints.
4. No saints were martyrs.
5. All martyrs were nonsaints.
6. Some nonmartyrs were saints.
7. Some saints were not nonmartyrs.
8. No martyrs were saints.
9. Some nonsaints were martyrs.
10. Some martyrs were nonsaints.
11. Some saints were not martyrs.
12. Some martyrs were not saints.
13. No saints were nonmartyrs.
14. No nonsaints were martyrs.
15. Some martyrs were not nonsaints.
5.8 INSTRUCTIONS
Express each of the following propositions as equalities or inequalities, representing each class by the first letter of the English term designating it, and symbolizing the proposition by means of a Venn diagram.
Example Problem
Some sculptors are painters.
Example Solution
1. No peddlers are millionaires.
2. All merchants are speculators.
3. Some musicians are not pianists.
4. Some political leaders of high reputation are scoundrels.
5. Some stockbrokers who advise their customers about making investments are not partners in companies whose securities they recommend.
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