Reasoning

Syllogism: Practice Questions with Answers

115 practice questions on Syllogism, with answers; most also have an explanation or a worked solution. Try each one before you open its answer.

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1. Q.1

   Statements: Some pens are books. All books are tables. Conclusions: I. Some pens are tables. II. Some tables are pens. Which conclusion(s) logically follow?

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   Answer: Both conclusions follow

   Solution:

   1. Some pens are books means the "pens" circle and "books" circle overlap. All books are tables means the "books" circle sits entirely inside the "tables" circle.
   2. The pens that overlap with books are therefore also inside tables — so some pens are tables. Conclusion I is forced.
   3. "Some pens are tables" (just shown true) can always be flipped to "Some tables are pens" — this flip is always valid for "Some…are" statements. So Conclusion II follows too.

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2. Q.2

   Statements: Some actors are singers. No singer is a dancer. Conclusions: I. No actor is a dancer. II. Some actors are dancers. Which conclusion(s) follow?

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   Answer: Either Conclusion I or Conclusion II follows

   Solution:

   1. The actors who are also singers are definitely not dancers (since no singer is a dancer). But non-singer actors are completely unconstrained — they could all be dancers, or none of them could.
   2. So Conclusion I ("No actor is a dancer") is too strong — it isn't forced. Conclusion II ("Some actors are dancers") also isn't forced — it's entirely possible that zero actors are dancers.
   3. But these two conclusions are exact complements: either SOME actor is a dancer, or NO actor is — one of the two must be true. Since neither follows alone but one of them must hold, the answer is "Either I or II follows."

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3. Q.3

   Statements: All cats are dogs. All dogs are cows. Conclusions: I. All cats are cows. II. All cows are cats. Which conclusion(s) logically follow?

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   Answer: Only Conclusion I follows

   Solution:

   1. All cats are dogs means the "cats" circle sits entirely inside the "dogs" circle. All dogs are cows means the "dogs" circle sits entirely inside the "cows" circle.
   2. So the "cats" circle is entirely inside the "cows" circle too — Conclusion I is forced in every possible arrangement.
   3. Conclusion II is not forced — the "cows" circle could easily be much bigger, containing cows that are neither dogs nor cats. It does not follow.

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4. Q.4

   Statements: No apples are oranges. Some oranges are fruits. Conclusions: I. Some fruits are not apples. II. No apples are fruits. Which conclusion(s) logically follow?

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   Answer: Only Conclusion I follows

   Solution:

   1. No apples are oranges means the "apples" circle and "oranges" circle do not overlap at all.
   2. Some oranges are fruits means part of the "oranges" circle overlaps with the "fruits" circle — and that overlapping part, being entirely within oranges, cannot contain any apples (since apples and oranges never overlap).
   3. So those particular fruits (the ones that are oranges) are definitely not apples — "Some fruits are not apples" is forced. Conclusion I follows.
   4. "No apples are fruits" is not forced — apples could still overlap with fruits through some path that has nothing to do with oranges; nothing in the statements rules that out. Conclusion II does not follow.

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5. Q.5

   Statements: All mangoes are fruits. All fruits are healthy foods. Some healthy foods are expensive. Conclusion: Some mangoes are expensive. Does it follow?

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   Answer: Does not follow

   Solution:

   1. Combining the first two statements: all mangoes are healthy foods (mangoes sit entirely inside healthy foods).
   2. But "some healthy foods are expensive" only guarantees an overlap SOMEWHERE inside healthy foods — that overlap might sit entirely outside the mango subset.
   3. So "Some mangoes are expensive" is not forced — it does not follow.

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6. Q.6

   Statements: All mangoes are fruits. All fruits are healthy foods. All healthy foods are nutritious. Conclusion: All mangoes are nutritious. Does it follow?

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   Answer: Follows

   Solution:

   1. This chain is "All...All...All" throughout, so transitivity carries all the way through: mangoes ⊆ fruits ⊆ healthy foods ⊆ nutritious things.
   2. So all mangoes are nutritious — the conclusion follows.

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7. Q.7

   Statements: All books are pens. No pen is a pencil. Conclusions: I. No book is a pencil. II. Some pens are books. Which conclusion(s) logically follow?

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   Answer: Both conclusions follow

   Solution:

   1. All books are pens means the "books" circle sits entirely inside the "pens" circle. No pen is a pencil means the "pens" circle and "pencils" circle do not overlap at all.
   2. Since the "books" circle is entirely inside the "pens" circle, and the "pens" circle never touches the "pencils" circle, the "books" circle can’t touch the "pencils" circle either — "No book is a pencil" is forced. Conclusion I follows.
   3. "All books are pens" guarantees every book is a pen, and since books exist, at least some pens are books — "Some pens are books" is forced. Conclusion II follows.

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8. Q.8

   Statements: All tigers are animals. All animals are living things. Some living things are plants. Conclusion: Some tigers are plants. Does it follow?

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   Answer: Does not follow — the "some living things are plants" overlap need not include any tigers.

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9. Q.9

   Statements: All squares are rectangles. All rectangles are polygons. Conclusions: I. All squares are polygons. II. Some polygons are squares. Which conclusion(s) follow?

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   Answer: Both conclusions follow

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10. Q.10

    Statements: Some pens are pencils. No pencil is an eraser. Conclusions: I. No pen is an eraser. II. Some pens are erasers. Which conclusion(s) follow?

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    Answer: Either Conclusion I or II follows (they are exact complements, and one must be true).

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11. Q.11

    Statements: All doctors are educated. All educated people are respected. Conclusions: I. All doctors are respected. II. Some respected people are doctors. Which conclusion(s) follow?

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    Answer: Both follow — I by transitivity, II by converting "All doctors are respected" to "Some respected are doctors."

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12. Q.12

    Statements: All mobiles are laptops. Some laptops are tablets. Conclusions: I. Some mobiles are tablets. II. Some tablets are mobiles. Which conclusion(s) follow?

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    Answer: Neither conclusion follows (the "some laptops are tablets" overlap need not touch mobiles at all)

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13. Q.13

    Statements: All tigers are animals. All animals are living things. All living things need oxygen. Conclusion: All tigers need oxygen. Does it follow?

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    Answer: Follows — an unbroken "All" chain carries transitivity all the way through.

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14. Q.14

    Statements: Some doctors are engineers. No engineer is a teacher. Conclusions: I. Some doctors are not teachers. II. No doctor is a teacher. Which conclusion(s) follow?

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    Answer: Only Conclusion I follows

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15. Q.15

    Statements: All roses are flowers. No weeds are flowers. Conclusions: I. No roses are weeds. II. No weeds are roses. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (A) Both conclusions follow

    Since all roses are flowers and no weeds are flowers, no rose can be a weed — this gives 'no roses are weeds', and since 'no X are Y' always implies 'no Y are X', 'no weeds are roses' follows too. Both conclusions follow.

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16. Q.16

    Statements: Some bicycles are scooters. Some scooters are not vehicles. Conclusions: I. All vehicles are bicycles. II. No bicycles are vehicles. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: Some bicycles are scooters. Some scooters are not vehicles. Conclusion I (All vehicles are bicycles) does not follow in every valid diagram consistent with the statements. Conclusion II (No bicycles are vehicles) does not follow.

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17. Q.17

    Statements: No tigers are rabbits. Some tigers are carnivores. Conclusions: I. Some carnivores are not rabbits. II. No carnivores are rabbits. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (B) Only conclusion I follows

    The tigers who are carnivores cannot be rabbits (since no tigers are rabbits) — so at least some carnivores are definitely not rabbits, which is Conclusion I. This says nothing about the OTHER carnivores (the ones that aren't tigers), so the stronger, blanket claim 'no carnivores are rabbits' in Conclusion II isn't forced.

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18. Q.18

    Statements: No actors are singers. All dancers are singers. Conclusions: I. No dancers are actors. II. No actors are dancers. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (A) Both conclusions follow

    Since all dancers are singers and no actors are singers, no dancer can be an actor — this gives both 'no dancers are actors' and, since 'no X are Y' always implies 'no Y are X', also 'no actors are dancers'. Both conclusions follow.

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19. Q.19

    Statements: All mobiles are laptops. Some laptops are tablets. Conclusions: I. Some mobiles are tablets. II. Some tablets are mobiles. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    The laptops that are tablets need not be the same laptops that are mobiles - the "some laptops are tablets" overlap doesn't have to touch mobiles at all. Neither conclusion is forced.

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20. Q.20

    Statements: Some pens are books. All books are tables. Conclusions: I. Some pens are tables. II. Some tables are pens. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (C) Both conclusions follow

    The pens that overlap with books are also inside tables, so some pens are tables is forced. Since this is a "some...are" statement, it converts validly to some tables are pens, so both follow.

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21. Q.21

    Statements: All cats are dogs. All dogs are pets. Conclusions: I. Some pets are cats. II. No pets are cats. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (B) Only conclusion I follows

    Statements: All cats are dogs. All dogs are pets. Conclusion I (Some pets are cats) follows: every cat is a dog and hence a pet, and at least one cat exists (these questions assume every named category has members), so at least one pet is a cat. Conclusion II (No pets are cats) does not follow — it is in fact contradicted, because that cat is a pet.

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22. Q.22

    Statements: No actors are directors. Some directors are not producers. Conclusions: I. All producers are actors. II. No producers are actors. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: No actors are directors. Some directors are not producers. Conclusion I (All producers are actors) does not follow in every valid diagram consistent with the statements. Conclusion II (No producers are actors) does not follow.

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23. Q.23

    Statements: All poets are artists. No artists are musicians. Conclusions: I. No poets are musicians. II. Some musicians are poets. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (B) Only conclusion I follows

    Statements: All poets are artists. No artists are musicians. Conclusion I (No poets are musicians) follows in every valid diagram consistent with the statements. Conclusion II (Some musicians are poets) does not follow.

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24. Q.24

    Statements: No guards are criminals. All guards are officers. Conclusions: I. Some officers are not criminals. II. No officers are criminals. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (A) Only conclusion I follows

    Every guard is an officer and no guard is a criminal, and, as these questions always assume, at least one guard exists - so that guard is an officer who is not a criminal, and 'some officers are not criminals' (Conclusion I) follows. 'No officers are criminals' (Conclusion II) is not forced: officers who are not guards could still be criminals.

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25. Q.25

    Statements: Some volcanoes are not mountains. All mountains are peaks. Conclusions: I. Some volcanoes are peaks. II. Some volcanoes are not peaks. Which of the conclusions logically follow?

    1. A Either conclusion I or II follows
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (A) Either conclusion I or II follows

    Statements: Some volcanoes are not mountains. All mountains are peaks. Conclusion I (Some volcanoes are peaks) does not follow — the volcanoes could all lie outside peaks. Conclusion II (Some volcanoes are not peaks) does not follow either — the non-mountain volcanoes could still be peaks. But the two conclusions share the same subject and predicate and are complementary: every volcano is either a peak or not, so at least one of 'some volcanoes are peaks' and 'some volcanoes are not peaks' must be true. Hence either Conclusion I or II follows.

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26. Q.26

    Statements: No rivers are mountains. No mountains are deserts. Conclusions: I. No rivers are deserts. II. Some rivers are deserts. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Either conclusion I or II follows
    4. D Neither conclusion follows
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    Correct answer: (C) Either conclusion I or II follows

    Two negative statements never force a valid conclusion about the two outer terms - rivers and deserts could overlap completely, partially, or not at all, so neither conclusion follows on its own. But the two conclusions are exact complements with the same subject and predicate: either some river is a desert or no river is, so one of them must be true. Hence either Conclusion I or II follows.

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27. Q.27

    Statements: Some clerks are managers. All clerks are employees. Conclusions: I. Some employees are managers. II. Some managers are employees. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (A) Both conclusions follow

    The clerks who are managers are also, by the second statement, employees — so these same people prove both 'some employees are managers' (Conclusion I) and 'some managers are employees' (Conclusion II, the same fact stated the other way round). Both follow.

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28. Q.28

    Statements: No novels are poems. Some poems are books. Conclusions: I. No books are novels. II. Some books are novels. Which of the conclusions logically follow?

    1. A Either conclusion I or II follows
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (A) Either conclusion I or II follows

    Statements: No novels are poems. Some poems are books. Conclusion I (No books are novels) does not follow — the books that are not poems could be novels. Conclusion II (Some books are novels) does not follow either — the books could all be poems, hence not novels. But the two conclusions share the same subject and predicate and are exact complements: either some book is a novel or no book is, so one of them must be true. Hence either Conclusion I or II follows.

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29. Q.29

    Statements: No novels are poems. Some poems are books. Conclusions: I. Some books are not novels. II. No books are novels. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (B) Only conclusion I follows

    Statements: No novels are poems. Some poems are books. Conclusion I (Some books are not novels) follows in every valid diagram consistent with the statements. Conclusion II (No books are novels) does not follow.

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30. Q.30

    Statements: All squares are rectangles. All rectangles are polygons. Conclusions: I. All squares are polygons. II. Some polygons are squares. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (C) Both conclusions follow

    All squares are rectangles and all rectangles are polygons combine transitively, so all squares are polygons is forced - Conclusion I follows. Since every square is a polygon and, as these questions always assume, at least one square exists, at least one polygon is a square - 'Some polygons are squares' follows as well. Both conclusions follow.

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31. Q.31

    Statements: All editors are writers. No writers are journalists. Conclusions: I. No journalists are editors. II. Some editors are journalists. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (B) Only conclusion I follows

    Statements: All editors are writers. No writers are journalists. Conclusion I (No journalists are editors) follows in every valid diagram consistent with the statements. Conclusion II (Some editors are journalists) does not follow.

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32. Q.32

    Statements: All painters are artists. No artists are lawyers. Conclusions: I. No painters are lawyers. II. Some painters are not lawyers. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (C) Both conclusions follow

    All painters are artists and no artist is a lawyer, so no painter can be a lawyer - Conclusion I follows. Since no painter is a lawyer and, as these questions always assume, at least one painter exists, at least some painters are not lawyers - Conclusion II follows as well. Both conclusions follow.

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33. Q.33

    Statements: All singers are dancers. Some dancers are performers. Conclusions: I. All singers are performers. II. No performers are singers. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: All singers are dancers. Some dancers are performers. Conclusion I (All singers are performers) does not follow in every valid diagram consistent with the statements. Conclusion II (No performers are singers) does not follow.

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34. Q.34

    Statements: No athletes are runners. All runners are swimmers. Conclusions: I. No swimmers are athletes. II. All swimmers are athletes. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: No athletes are runners. All runners are swimmers. Conclusion I (No swimmers are athletes) does not follow in every valid diagram consistent with the statements. Conclusion II (All swimmers are athletes) does not follow.

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35. Q.35

    Statements: No violins are cellos. All cellos are stringinstruments. Conclusions: I. No stringinstruments are violins. II. Some stringinstruments are violins. Which of the conclusions logically follow?

    1. A Either conclusion I or II follows
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (A) Either conclusion I or II follows

    Statements: No violins are cellos. All cellos are stringinstruments. Conclusion I (No stringinstruments are violins) does not follow — violins could be stringinstruments without being cellos. Conclusion II (Some stringinstruments are violins) does not follow either — violins could lie entirely outside stringinstruments. But the two conclusions share the same subject and predicate and are exact complements: either some stringinstrument is a violin or none is, so one of them must be true. Hence either Conclusion I or II follows.

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36. Q.36

    Statements: Some tablets are not cameras. Some cameras are not devices. Conclusions: I. No devices are tablets. II. Some devices are not tablets. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: Some tablets are not cameras. Some cameras are not devices. Conclusion I (No devices are tablets) does not follow in every valid diagram consistent with the statements. Conclusion II (Some devices are not tablets) does not follow.

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37. Q.37

    Statements: Some writers are poets. No poets are bankers. Conclusions: I. No writers are bankers. II. Some writers are not bankers. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (B) Only conclusion II follows

    Some writers are poets, and no poet is a banker, so the writers who are poets cannot be bankers - 'some writers are not bankers' (Conclusion II) is forced. 'No writer is a banker' (Conclusion I) is too strong, since writers outside the poet overlap could still be bankers.

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38. Q.38

    Statements: No hills are deserts. All mountains are hills. Conclusions: I. Some mountains are not deserts. II. No mountains are deserts. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (C) Both conclusions follow

    Since no hills are deserts and all mountains are hills, no mountain can be a desert - Conclusion II follows. Conclusion I is the weaker claim that at least some mountains are not deserts: since no mountain is a desert and, as these questions always assume, at least one mountain exists, it follows too. Both conclusions follow.

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39. Q.39

    Statements: Some chefs are not bakers. Some bakers are waiters. Conclusions: I. Some waiters are chefs. II. Some chefs are not waiters. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: Some chefs are not bakers. Some bakers are waiters. Conclusion I (Some waiters are chefs) does not follow in every valid diagram consistent with the statements. Conclusion II (Some chefs are not waiters) does not follow.

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40. Q.40

    Statements: Some actors are directors. All directors are producers. Conclusions: I. No producers are actors. II. Some actors are producers. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (C) Only conclusion II follows

    Statements: Some actors are directors. All directors are producers. Conclusion I (No producers are actors) does not follow in every valid diagram consistent with the statements. Conclusion II (Some actors are producers) follows.

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41. Q.41

    Statements: All violins are cellos. Some cellos are stringinstruments. Conclusions: I. No stringinstruments are violins. II. Some violins are not stringinstruments. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
    Show answer

    Correct answer: (D) Neither conclusion follows

    Statements: All violins are cellos. Some cellos are stringinstruments. Conclusion I (No stringinstruments are violins) does not follow in every valid diagram consistent with the statements. Conclusion II (Some violins are not stringinstruments) does not follow.

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42. Q.42

    Statements: All books are pens. No pen is a pencil. Conclusions: I. No book is a pencil. II. Some pens are books. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (C) Both conclusions follow

    Since all books are pens and no pen is a pencil, no book can be a pencil - Conclusion I follows. For Conclusion II: every book is a pen and, as these questions always assume, at least one book exists, so at least one pen is a book - 'Some pens are books' follows too. Both conclusions follow.

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43. Q.43

    Statements: Some painters are not sculptors. All musicians are sculptors. Conclusions: I. No painters are musicians. II. Some painters are not musicians. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (C) Only conclusion II follows

    The painters who are not sculptors also cannot be musicians (since every musician is a sculptor) — so at least some painters are definitely not musicians, which is Conclusion II. But Conclusion I's blanket claim that NO painter is a musician isn't forced, since the OTHER painters (who are sculptors) could still include some musicians.

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44. Q.44

    Statements: Some farmers are not gardeners. Some gardeners are not cultivators. Conclusions: I. No cultivators are farmers. II. All farmers are cultivators. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: Some farmers are not gardeners. Some gardeners are not cultivators. Conclusion I (No cultivators are farmers) does not follow in every valid diagram consistent with the statements. Conclusion II (All farmers are cultivators) does not follow.

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45. Q.45

    Statements: All singers are dancers. All dancers are performers. Conclusions: I. Some performers are not singers. II. No performers are singers. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
    Show answer

    Correct answer: (D) Neither conclusion follows

    Statements: All singers are dancers. All dancers are performers. Conclusion I (Some performers are not singers) does not follow in every valid diagram consistent with the statements. Conclusion II (No performers are singers) does not follow.

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46. Q.46

    Statements: No farmers are villagers. All landlords are farmers. Conclusions: I. Some landlords are not villagers. II. No landlords are villagers. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (C) Both conclusions follow

    Since no farmers are villagers and all landlords are farmers, no landlord can be a villager - Conclusion II follows. Conclusion I is the weaker claim that at least some landlords are not villagers: since no landlord is a villager and, as these questions always assume, at least one landlord exists, it follows too. Both conclusions follow.

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47. Q.47

    Statements: All canals are streams. All rivers are canals. Conclusions: I. All rivers are streams. II. Some streams are rivers. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (C) Both conclusions follow

    All canals are streams and all rivers are canals combine transitively, so all rivers are streams is forced - Conclusion I follows. Since every river is a stream and, as these questions always assume, at least one river exists, at least one stream is a river - 'Some streams are rivers' follows too. Both conclusions follow.

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48. Q.48

    Statements: All umbrellas are raincoats. Some raincoats are rainwear. Conclusions: I. Some umbrellas are rainwear. II. No rainwear are umbrellas. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    Statements: All umbrellas are raincoats. Some raincoats are rainwear. Conclusion I (Some umbrellas are rainwear) does not follow in every valid diagram consistent with the statements. Conclusion II (No rainwear are umbrellas) does not follow.

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49. Q.49

    Statements: Some bicycles are not scooters. All scooters are vehicles. Conclusions: I. Some vehicles are not bicycles. II. All bicycles are vehicles. Which of the conclusions logically follow?

    1. A Both conclusions follow
    2. B Only conclusion I follows
    3. C Only conclusion II follows
    4. D Neither conclusion follows
    Show answer

    Correct answer: (D) Neither conclusion follows

    Statements: Some bicycles are not scooters. All scooters are vehicles. Conclusion I (Some vehicles are not bicycles) does not follow in every valid diagram consistent with the statements. Conclusion II (All bicycles are vehicles) does not follow.

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50. Q.50

    Statements: Some singers are not dancers. Some dancers are musicians. Conclusions: I. Some singers are musicians. II. Some musicians are not singers. Which of the conclusions logically follow?

    1. A Only conclusion I follows
    2. B Only conclusion II follows
    3. C Both conclusions follow
    4. D Neither conclusion follows
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    Correct answer: (D) Neither conclusion follows

    A particular-negative statement combined with a particular-positive statement never forces a valid conclusion about the two outer terms here - neither conclusion follows.

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