Syllogisms Questions and Answers

Q: Statements: All green are blue. All blue are white. Conclusions: 1. Some blue are green. 2. Some white are green. 3. Some green are not white. 4. All white are blue.

Correct answer: Only (1) and (2)All green are blue gives some blue are green, conclusion 1; and since all green are blue and all blue are white, all green are white, whence some white are green, conclusion 2. Conclusion 3 contradicts that, and conclusion 4 reverses a universal.

Q: Statements: All men are vertebrates. Some mammals are vertebrates. Conclusions: 1. All men are mammals. 2. All mammals are men. 3. Some vertebrates are mammals. 4. All vertebrates are men.

Correct answer: Only (3)Some mammals are vertebrates gives its converse, some vertebrates are mammals. The other three try to link men with mammals, and the only connection is through vertebrates as a predicate in both statements - an undistributed middle, which proves nothing.

Q: Statements: All the phones are scales. All the scales are calculators. Conclusions: 1. All the calculators are scales. 2. All the phones are calculators 3. All the scales are phones. 4. Some calculators are phones.

Correct answer: Only (2) and (4)All phones are scales and all scales are calculators, so all phones are calculators - conclusion 2 - and therefore some calculators are phones, conclusion 4. Conclusions 1 and 3 reverse universals, which is never valid.

Q: Statements: Some tables are T.V. Some T.V. are radios. Conclusions: 1. Some tables are radios. 2. Some radios are tables. 3. All the radios are T.V. 4. All the T.V. are tables.

Correct answer: None of the four.Both statements are particular - some tables are T.V., some T.V. are radios - and the televisions in the two need not be the same, so nothing links tables to radios. The remaining conclusions turn particulars into universals. None of the four follows.

Q: Statements: Some pens are books. Some books are pencils. Conclusions: 1. Some pens are pencils. 2. Some pencils are pens. 3. All pencils are pens. 4. All books are pens.

Correct answer: None of the fourBoth statements are particular, and the books that are pens need not be the books that are pencils, so nothing links pens to pencils. Conclusions 3 and 4 make universals out of particulars. None of the four follows.

Q: Statements: All the goats are tigers. All the tigers are lions. Conclusions: 1. All the goats are lions. 2. All the lions are goats. 3. Some lions are goats. 4. Some tigers are goats.

Correct answer: Only (1), (3) and (4)All goats are tigers and all tigers are lions, so all goats are lions - conclusion 1 - and its converse, some lions are goats, conclusion 3. All goats being tigers also gives some tigers are goats, conclusion 4. Only conclusion 2 fails, reversing a universal.

Q: Statements: All the books are pencils. No pencil is eraser. Conclusions: 1. All the pencils are books. 2. Some erasers are books. 3. No book is eraser. 4. Some books are erasers.

Correct answer: Only (3)All books are pencils and no pencil is an eraser, so nothing that is a book can be an eraser - no book is an eraser, conclusion 3. Conclusions 2 and 4 assert the opposite, and conclusion 1 reverses a universal.

Q: Statements: All the research scholars are psychologists. Some psychologists are scientists. Conclusions: 1. All the research scholars are scientists. 2. Some research scholars are scientists. 3. Some scientists are psychologists. 4. Some psychologists are research scholars.

Correct answer: Only (3) and (4)Some psychologists are scientists gives its converse, some scientists are psychologists - conclusion 3; and all research scholars being psychologists gives some psychologists are research scholars, conclusion 4. Conclusions 1 and 2 need the psychologists who are scientists to be the research scholars, which is not given.

Q: Statements: All the locks are keys. All the keys are bats. Some watches are bats. Conclusions: 1. Some bats are locks. 2. Some watches are keys. 3. All the keys are locks.

Correct answer: Only (1)All locks are keys and all keys are bats, so all locks are bats - and therefore some bats are locks, conclusion 1. Conclusion 2 needs the bats that are watches to be keys, which is not given, and conclusion 3 reverses a universal.

Q: Statements: Some keys are staplers. Some staplers are stickers. All the stickers are pens. Conclusions: 1. Some pens are staplers. 2. Some stickers are keys. 3. No sticker is key. 4. Some staplers are keys.

Correct answer: Only (1) and (4) and either (2) or (3)Some staplers are stickers and all stickers are pens, so some pens are staplers - conclusion 1; and some keys being staplers gives some staplers are keys, conclusion 4. Conclusions 2 and 3 concern stickers and keys, which the statements leave open - but between them they cover both possibilities, so either holds.

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71.

Statements: All green are blue. All blue are white.

Conclusions:

1. Some blue are green.

2. Some white are green.

3. Some green are not white.

4. All white are blue.

A.Only (1) and (2)
B.Only (1) and (3)
C.Only (1) and (4)
D.Only (2) and (4)

Answer: A

Correct answer: Only (1) and (2)

All green are blue gives some blue are green, conclusion 1; and since all green are blue and all blue are white, all green are white, whence some white are green, conclusion 2. Conclusion 3 contradicts that, and conclusion 4 reverses a universal.

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72.

Statements: All men are vertebrates. Some mammals are vertebrates.

Conclusions:

1. All men are mammals.

2. All mammals are men.

3. Some vertebrates are mammals.

4. All vertebrates are men.

A.Only (4)
B.Only (2)
C.Only (3)
D.Only (1)

Answer: C

Correct answer: Only (3)

Some mammals are vertebrates gives its converse, some vertebrates are mammals. The other three try to link men with mammals, and the only connection is through vertebrates as a predicate in both statements - an undistributed middle, which proves nothing.

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73.

Statements: All the phones are scales. All the scales are calculators.

Conclusions:

1. All the calculators are scales.

2. All the phones are calculators

3. All the scales are phones.

4. Some calculators are phones.

A.Only (1) and (4)
B.Only (3) and (4)
C.Only (2) and (4)
D.Only (1) and (2)

Answer: C

Correct answer: Only (2) and (4)

All phones are scales and all scales are calculators, so all phones are calculators - conclusion 2 - and therefore some calculators are phones, conclusion 4. Conclusions 1 and 3 reverse universals, which is never valid.

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74.

Statements: Some tables are T.V. Some T.V. are radios.

Conclusions:

1. Some tables are radios.

2. Some radios are tables.

3. All the radios are T.V.

4. All the T.V. are tables.

A.Only (2) and (4)
B.Only (1) and (3)
C.Only (4)
D.None of the four.

Answer: D

Correct answer: None of the four.

Both statements are particular - some tables are T.V., some T.V. are radios - and the televisions in the two need not be the same, so nothing links tables to radios. The remaining conclusions turn particulars into universals. None of the four follows.

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75.

Statements: Some pens are books. Some books are pencils.

Conclusions:

1. Some pens are pencils.

2. Some pencils are pens.

3. All pencils are pens.

4. All books are pens.

A.Only (1) and (3)
B.Only (2) and (4)
C.All the four
D.None of the four

Answer: D

Correct answer: None of the four

Both statements are particular, and the books that are pens need not be the books that are pencils, so nothing links pens to pencils. Conclusions 3 and 4 make universals out of particulars. None of the four follows.

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76.

Statements: All the goats are tigers. All the tigers are lions.

Conclusions:

1. All the goats are lions.

2. All the lions are goats.

3. Some lions are goats.

4. Some tigers are goats.

A.All the four
B.Only (1), (2) and (3)
C.Only (1), (3) and (4)
D.Only (2), (3) and (4)

Answer: C

Correct answer: Only (1), (3) and (4)

All goats are tigers and all tigers are lions, so all goats are lions - conclusion 1 - and its converse, some lions are goats, conclusion 3. All goats being tigers also gives some tigers are goats, conclusion 4. Only conclusion 2 fails, reversing a universal.

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77.

Statements: All the books are pencils. No pencil is eraser.

Conclusions:

1. All the pencils are books.

2. Some erasers are books.

3. No book is eraser.

4. Some books are erasers.

A.Only (3)
B.Only (1) and (3)
C.Only (1) and (2)
D.Only (2) and (3)

Answer: A

Correct answer: Only (3)

All books are pencils and no pencil is an eraser, so nothing that is a book can be an eraser - no book is an eraser, conclusion 3. Conclusions 2 and 4 assert the opposite, and conclusion 1 reverses a universal.

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78.

Statements: All the research scholars are psychologists. Some psychologists are scientists.

Conclusions:

1. All the research scholars are scientists.

2. Some research scholars are scientists.

3. Some scientists are psychologists.

4. Some psychologists are research scholars.

A.Only (3) and (4)
B.None of the four
C.All the four
D.Only (3)

Answer: A

Correct answer: Only (3) and (4)

Some psychologists are scientists gives its converse, some scientists are psychologists - conclusion 3; and all research scholars being psychologists gives some psychologists are research scholars, conclusion 4. Conclusions 1 and 2 need the psychologists who are scientists to be the research scholars, which is not given.

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79.

Statements: All the locks are keys. All the keys are bats. Some watches are bats.

Conclusions:

1. Some bats are locks.

2. Some watches are keys.

3. All the keys are locks.

A.Only (1) and (2)
B.Only (1)
C.Only (2)
D.Only (1) and (3)

Answer: B

Correct answer: Only (1)

All locks are keys and all keys are bats, so all locks are bats - and therefore some bats are locks, conclusion 1. Conclusion 2 needs the bats that are watches to be keys, which is not given, and conclusion 3 reverses a universal.

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80.

Statements: Some keys are staplers. Some staplers are stickers. All the stickers are pens.

Conclusions:

1. Some pens are staplers.

2. Some stickers are keys.

3. No sticker is key.

4. Some staplers are keys.

A.Only (1) and (2)
B.Only (2) and (4)
C.Only (2) and (3)
D.Only (1) and (4) and either (2) or (3)

Answer: D

Correct answer: Only (1) and (4) and either (2) or (3)

Some staplers are stickers and all stickers are pens, so some pens are staplers - conclusion 1; and some keys being staplers gives some staplers are keys, conclusion 4. Conclusions 2 and 3 concern stickers and keys, which the statements leave open - but between them they cover both possibilities, so either holds.

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