| Phil. 1: Introduction to Logic | |
| Schedule | |
| Answer Key | |
1. All people who made lots of money on the stock market are inside traders.
All persons identical to Ivan Boesky are people who made lots of money on the stock market.
Therefore, all people identical to Ivan Boesky are inside traders.
Valid
2. All times suicide rates decline are times people's lives are better adjusted.
All recent years are times suicide rates decline.
Therefore, all recent years are times people's lives are better adjusted.
Valid
3. All cars purchased by environmentalists are fuel- efficient cars.
No Rolls Royces are cars purchased by environmentalists.
Therefore, no Rolls Royces are fuel-efficient cars.
Invalid, illicit major
4. All quarterbacks who led their team to four Super Bowl victories are athletes who deserve to be in the football hall of fame.
All persons identical to Joe Montana are athletes who deserve to be in the football hall of fame.
Therefore, All persons identical to Joe Montana are quarterbacks who led their team to four Super Bowl victories.
Invalid, undistributed middle
5. All institutions that teach secular humanism are institutions that teach religion.
Some public schools are institutions that teach secular humanism.
Therefore, some public schools are institutions that teach religion.
Valid
6. All persons who support tobacco subsidies by the government are persons who support tobacco-related health hazards.
All persons identical to Senator Jesse Helms are persons who support tobacco subsidies by the government.
Therefore, all persons identical to Senator Jesse Helms are persons who support tobacco-related health hazards.
Valid
7. Some songs Kathleen Battle sings are Puccini arias.
All songs Kathleen Battle wants to sing are songs Kathleen Battle sings.
Therefore, some songs Kathleen Battle wants to sing are Puccini arias.
Invalid, undistributed middle
8. Some interest expenses are not tax-deductible expenses.
All home mortgage expenses are interest expenses.
Therefore, no home mortgage expenses are tax-deductible expenses.
Invalid, undistributed middle
9. All marriages that allow little room for growth are arrangements bound to fail.
All marriages based on a meshing of neuroses are marriages that allow little room for growth.
Therefore, all marriages based on a meshing of neuroses are arrangements bound to fail.
Valid
10. All TV viewers who receive scrambled signals are viewers with a decoder.
All persons who receive digital satellite signals are TV viewers who receive scrambled signals.
Therefore, all persons who receive digital satellite signals are viewers with a decoder.
Valid
11. All countries where the national diet is rich in wheat bran are countries where the incidence of colon cancer is low.
No countries identical to Canada are countries where the national diet is rich in wheat bran.
Therefore, no countries identical to Canada are countries where the incidence of colon cancer is low.
Invalid, illicit major
12. All persons who think Africa is in North America are persons with no knowledge of geography.
Some college students are persons who think Africa is in North America.
Therefore, some college students are persons with no knowledge of geography.
Valid
13. All diseases carried by recessive genes are diseases that can be inherited by offspring of two carriers.
All diseases identical to cystic fibrosis are diseases carried by recessive genes.
Therefore, all diseases identical to cystic fibrosis are diseases that can be inherited by offspring of two carriers.
Valid
14. Since the first premise is an exceptive proposition, we have two arguments:
No metals identical to mercury are solids at room temperature.
No metals identical to cadmium are metals identical to mercury.
Therefore, all metals identical to cadmium are solids at room temperature.
Invalid, exclusive premises
All metals not identical to mercury are solids at room temperature.
All metals identical to cadmium are metals not identical to mercury.
Therefore, all metals identical to cadmium are solids at room temperature.
Valid
Since one of the two arguments is valid, the original argument is valid.
15. Some times are times aversive therapy is inhumane.
Some times are times autistic children are helped by aversive therapy.
Therefore, some times autistic children are helped by aversive therapy are times aversive t herapy is inhumane.
Invalid, undistributed middle
Exercise 5.51. All people who made lots of money on the stock market are inside traders.
All persons identical to Ivan Boesky are people who made lots of money on the stock market.
Therefore, all people identical to Ivan Boesky are inside traders.
Valid
2. All times suicide rates decline are times people's lives are better adjusted.
All recent years are times suicide rates decline.
Therefore, all recent years are times people's lives are better adjusted.
Valid
3. All cars purchased by environmentalists are fuel- efficient cars.
No Rolls Royces are cars purchased by environmentalists.
Therefore, no Rolls Royces are fuel-efficient cars.
Invalid, illicit major
4. All quarterbacks who led their team to four Super Bowl victories are athletes who deserve to be in the football hall of fame.
All persons identical to Joe Montana are athletes who deserve to be in the football hall of fame.
Therefore, All persons identical to Joe Montana are quarterbacks who led their team to four Super Bowl victories.
Invalid, undistributed middle
5. All institutions that teach secular humanism are institutions that teach religion.
Some public schools are institutions that teach secular humanism.
Therefore, some public schools are institutions that teach religion.
Valid
6. All persons who support tobacco subsidies by the government are persons who support tobacco-related health hazards.
All persons identical to Senator Jesse Helms are persons who support tobacco subsidies by the government.
Therefore, all persons identical to Senator Jesse Helms are persons who support tobacco-related health hazards.
Valid
7. Some songs Kathleen Battle sings are Puccini arias.
All songs Kathleen Battle wants to sing are songs Kathleen Battle sings.
Therefore, some songs Kathleen Battle wants to sing are Puccini arias.
Invalid, undistributed middle
8. Some interest expenses are not tax-deductible expenses.
All home mortgage expenses are interest expenses.
Therefore, no home mortgage expenses are tax-deductible expenses.
Invalid, undistributed middle
9. All marriages that allow little room for growth are arrangements bound to fail.
All marriages based on a meshing of neuroses are marriages that allow little room for growth.
Therefore, all marriages based on a meshing of neuroses are arrangements bound to fail.
Valid
10. All TV viewers who receive scrambled signals are viewers with a decoder.
All persons who receive digital satellite signals are TV viewers who receive scrambled signals.
Therefore, all persons who receive digital satellite signals are viewers with a decoder.
Valid
11. All countries where the national diet is rich in wheat bran are countries where the incidence of colon cancer is low.
No countries identical to Canada are countries where the national diet is rich in wheat bran.
Therefore, no countries identical to Canada are countries where the incidence of colon cancer is low.
Invalid, illicit major
12. All persons who think Africa is in North America are persons with no knowledge of geography.
Some college students are persons who think Africa is in North America.
Therefore, some college students are persons with no knowledge of geography.
Valid
13. All diseases carried by recessive genes are diseases that can be inherited by offspring of two carriers.
All diseases identical to cystic fibrosis are diseases carried by recessive genes.
Therefore, all diseases identical to cystic fibrosis are diseases that can be inherited by offspring of two carriers.
Valid
14. Since the first premise is an exceptive proposition, we have two arguments:
No metals identical to mercury are solids at room temperature.
No metals identical to cadmium are metals identical to mercury.
Therefore, all metals identical to cadmium are solids at room temperature.
Invalid, exclusive premises
All metals not identical to mercury are solids at room temperature.
All metals identical to cadmium are metals not identical to mercury.
Therefore, all metals identical to cadmium are solids at room temperature.
Valid
Since one of the two arguments is valid, the original argument is valid.
15. Some times are times aversive therapy is inhumane.
Some times are times autistic children are helped by aversive therapy.
Therefore, some times autistic children are helped by aversive therapy are times aversive t herapy is inhumane.
Invalid, undistributed middle