Chapter 6 Answer Key to Select Chapter Exercises

Exercise 6.1
3. S = cats that have lived over fifteen years in a domestic setting; P = pets free of all health problems; universal negative; E
4. S = urbanites who wear lumberjack jackets and big bushy beards; P = hipsters; universal affirmative; A
9. S = taxpayers from the 2022 tax year; P = tax cheats; universal negative; E
10. S = Canadian banks that had dealings with Enron; P = institutions that deserve our business; universal negative; E
13. S = Indigenous groups; P = groups who have voluntarily given up their land; universal negative; E
15. S = people who sell homeopathic treatments; P = people who are delusional or fraudsters; universal affirmative; A

Exercise 6.2
3. Some professors are not engaging speakers. O
4. Some sharks are animals that will try to bite you if they get the chance. I
7. Some people with pinched faces are persons who have poisonous hearts. I
10. All things worth doing are things worth doing right. A
14. Some senior citizens are people who like rap music. I
15. No things that are excellent are things without difficulty. E

Exercise 6.3
2. All political parties that get less than 10 per cent of the vote in a general election are parties that should be considered minor players in Canadian politics. A
3. All persons who wish to salute the free and independent side of their evolutionary character are persons who acquire cats. A
7. All people who work hard are people who achieve a good command of categorical logic. A
10. All persons who have struggled with poverty are people who know how expensive it is to be poor. A
14. No people are people who can truly rest while poverty, injustice, and gross inequality persist in our world. E
16. No people I can really trust are people who were cool in their younger years. E
17. No persons being carried are persons who know how far the town is. E

Exercise 6.4
2. No person has the right to rain on your dreams. = No persons are persons with the right to rain on your dreams. S = persons; P = persons with the right to rain on your dreams.

A Venn diagram shows no S are P. Two circles labeled S and P intersects each other, the intersecting portion is shaded.

4. Some mammals live most of their lives in the water. = Some mammals are animals that live most of their lives in the water. S = mammals; P = animals that live most of their lives in the water.

A Venn diagram of some S are P. Two circles labeled S and P intersect each other. The intersecting portion is labeled as X.

6. One of the few philosophers whose ideas have truly shaped the modern world is Adam Smith. = Some persons whose ideas have truly shaped the modern world are philosophers identical with Adam Smith. S = philosophers whose ideas have shaped the modern world; P = all persons identical with Adam Smith.

7. Some books are not written by either J.K. Rowling or Stephen King. = Some books are not books written by either J.K. Rowling or Stephen King. S = books; P = books written by either J.K. Rowling or Stephen King.

A Venn diagram shows some S are not P. Two circles labeled S and P intersects each other, the S circle on the left is denoted as X.

10. Some people with excellent reputations are not persons of excellent character. S = people with excellent reputations; P = persons of excellent character.

15. Few friendships could survive the moodiness of love affairs. = Some friendships are not friendships that could survive the moodiness of love affairs. S = friendships; P = friendships that could survive the moodiness of love affairs.

Exercise 6.5
2. Equivalent

Two sets of Venn diagrams show some S are P on the left and some P are S on the right. Two circles labeled S and P intersects each other. The intersecting portions are labeled as X.

7. Not equivalent

Two sets of Venn diagrams. Two circles labeled S and P intersects each other. The circle P is shaded in the diagram on the left, and circle S is shaded in the diagram on the right.

10. Equivalent

Two sets of Venn diagrams show no S are P on the left and no P are S on the right. Two circles labeled S and P intersects each other. The intersecting portions are shaded.

Exercise 6.6
3. Some birds are parrots. All parrots make great pets. So some birds make great pets.
S = birds
P = animals that make great pets
M = parrots
Some S are M.
All M are P.
Therefore, some S are P.
4. All corporations are structured such that their owners have limited liability, but some businesses are not structured such that their owners have limited liability. Therefore some businesses are not corporations.
S = businesses
P = corporations
M = organizations structured such that their owners have limited liability
All P are M.
Some S are not M.
Therefore, some S are not P.
7. All banks are financial services companies. All financial services companies are highly regulated. So all banks are highly regulated.
S = banks
P = highly regulated things
M = financial services companies
All S are M.
All M are P.
Therefore, all S are P.
8. All roads are highways to Rome, but no mere paths are roads. So no mere paths are highways to Rome.
S = mere paths
P = highways to Rome
M = roads
All M are P.
No S are M.
Therefore, no S are P.

Exercise 6.7
3. Valid

A Venn diagram of 3 circles labeled M, S, and P that intersect. The section that overlaps between M, S, and P is denoted with and X. The sections that overlap between M; and M and S are shaded.

4. Valid

A Venn diagram of 3 circles labeled M, S, and P that intersect. S is denoted with and X. The sections that overlap between S and P; and section P are shaded.

7. Valid

A Venn diagram of 3 circles labeled M, S, and P that intersect. Sections M; overlap between M and S; S; and the overlap between S and P are shaded.

8. Invalid

A Venn diagram of 3 circles labeled M, S, and P that intersect. Sections M; the overlap between M and S; and the overlap between M, S, and P; are shaded.

Exercise 6.8
2. All (S) Doritos are (M) foods that are salty and high in fat.
All (M) foods that are salty and high in fat are (P) delicious foods.
Therefore, all (S) Doritos are (P) delicious foods.
All S are M.
All M are P.
Therefore, all S are P.

A Venn diagram of 3 circles labeled M, S, and P that intersect. Sections M; S; the overlap between M and S; and the overlap between S and P are shaded.

Valid
4. All (M) people who think meat production is environmentally sustainable are (P) people who are ill-informed. Some (S) people who eat meat are (M) people who think meat production is environmentally sustainable. So some (S) people who eat meat are (P) people who are ill-informed.
All M are P.
Some S are M.
Therefore some S are P.

A Venn diagram of 3 circles labeled M, S, and P that intersect. Sections M and the overlap between M and S are shaded. The overlap between M, S, and P is denoted with an X.

Valid
5. (Translating this one is tricky, due to the fact that some of the original sentences refer to patients while others refer to their organs.) All (S) organs of cancer patients are (M) organs that could contain cancer. No (M) organs that could contain cancer are (P) organs that doctors would allow to be donated. Therefore no (S) organs of cancer patients are (P) organs that doctors would allow to be donated.
All S are M.
No M are P.
Therefore, no S are P.

A Venn diagram of 3 circles labeled M, S, and P that intersect. Section S; the overlap between S and P; the overlap between M, S, and P; and the overlap between M and P are shaded.

Valid
10. (S) Vitamin pills are (M) useless gimmicks promoted as sure-cures for a variety of illnesses. Some (M) useless gimmicks promoted as sure-cures, though, are (P) placebos that can make people feel good even if they don’t cure anything. So some (S) vitamin pills are (P) placebos that can make people feel good even if they don’t cure anything.
All S are M.
Some M are P.
Therefore, some S are P.

A Venn diagram of 3 circles labeled M, S, and P that intersect. Sections S and the overlap between S and P are shaded. The line between S and the overlap between M and P is denoted with an X.

Invalid