Syllogism MCQs

Solved syllogism MCQs for IBPS, SBI and SSC: two statements, two conclusions, and the standard rules for all, some, no and either-or cases, explained with Venn-diagram reasoning.

1. 1

   Statements: All cats are dogs. All dogs are birds. Conclusions: I. All cats are birds. II. Some birds are cats.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: E. Both I and II are true

   Cats sit inside dogs, which sit inside birds, so all cats are birds. Since all cats are birds, some birds are cats too.

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2. 2

   Statements: Some pens are books. All books are bags. Conclusions: I. Some pens are bags. II. All bags are pens.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: A. Only conclusion I is true

   The pens that are books are also bags, so some pens are bags. Nothing tells us that every bag is a pen.

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3. 3

   Statements: No apple is a mango. All mangoes are fruits. Conclusions: I. No apple is a fruit. II. Some fruits are not apples.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: B. Only conclusion II is true

   Mangoes are fruits and no mango is an apple, so some fruits (the mangoes) are not apples. Apples could still be fruits, so I does not follow.

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4. 4

   Statements: Some chairs are tables. Some tables are doors. Conclusions: I. Some chairs are doors. II. No chair is a door.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: C. Either I or II is true

   Neither conclusion is certain, but they are about the same two groups and one of them must be true (some chairs are doors, or none are). This is an either-or case.

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5. 5

   Statements: All roses are flowers. Some flowers are red. Conclusions: I. Some roses are red. II. All flowers are roses.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: D. Neither I nor II is true

   The red flowers may or may not include roses, so I is not certain. Roses are only part of the flowers, so II is false.

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6. 6

   Statements: All teachers are educated. No educated person is lazy. Conclusions: I. No teacher is lazy. II. Some educated persons are teachers.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: E. Both I and II are true

   Teachers lie inside the educated group, which has no lazy people, so no teacher is lazy. All teachers being educated also means some educated persons are teachers.

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7. 7

   Statements: Some students are players. No player is lazy. Conclusions: I. Some students are not lazy. II. All students are lazy.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: A. Only conclusion I is true

   The students who are players cannot be lazy, so some students are not lazy. That also means II is false.

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8. 8

   Statements: All boxes are cartons. Some cartons are bags. Conclusions: I. Some boxes are bags. II. Some bags are boxes.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: D. Neither I nor II is true

   The cartons that are bags may not be boxes, so no link between boxes and bags is certain. Neither conclusion follows.

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9. 9

   Statements: No car is a bus. No bus is a train. Conclusions: I. No car is a train. II. Some cars are trains.

   AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

   Correct answer: C. Either I or II is true

   Two negative statements give no definite link between cars and trains. But I and II are about the same groups and exactly one must be true, so either I or II.

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10. 10

    Statements: All rivers are lakes. All lakes are seas. Conclusions: I. All seas are rivers. II. Some seas are rivers.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: B. Only conclusion II is true

    All rivers are seas, so some seas are rivers. But seas may include much more than rivers, so I does not follow.

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12. 11

    Statements: Some doctors are singers. All singers are dancers. Conclusions: I. Some dancers are doctors. II. Some doctors are dancers.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: E. Both I and II are true

    The doctors who are singers are also dancers, so some doctors are dancers, and therefore some dancers are doctors.

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13. 12

    Statements: All laptops are phones. No phone is a radio. Conclusions: I. No laptop is a radio. II. Some radios are laptops.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: A. Only conclusion I is true

    Laptops lie inside phones, and phones share nothing with radios, so no laptop is a radio. II contradicts this.

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14. 13

    Statements: Some books are pens. Some pens are erasers. Conclusions: I. Some books are erasers. II. All erasers are pens.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: D. Neither I nor II is true

    Two "some" statements give no certain link between books and erasers, and nothing says all erasers are pens.

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15. 14

    Statements: All buses are vans. All vans are trucks. Conclusions: I. Some trucks are buses. II. All trucks are vans.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: A. Only conclusion I is true

    All buses are trucks, so some trucks are buses. Trucks may include vehicles that are not vans, so II does not follow.

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16. 15

    Statements: No ink is a pen. Some pens are pencils. Conclusions: I. Some pencils are not inks. II. No pencil is an ink.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: A. Only conclusion I is true

    The pencils that are pens cannot be inks, so some pencils are not inks. Other pencils might be inks, so II is not certain.

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17. 16

    Statements: Some birds are eagles. All eagles are hunters. Conclusions: I. All birds are hunters. II. Some birds are hunters.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: B. Only conclusion II is true

    The birds that are eagles are hunters, so some birds are hunters. Nothing is said about the other birds, so I does not follow.

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18. 17

    Statements: All gold is metal. Some metal is costly. Conclusions: I. Some gold is costly. II. No gold is costly.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: C. Either I or II is true

    The costly metal may or may not be gold, so neither is certain. But I and II cover all possibilities for the same groups, so either I or II is true.

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19. 18

    Statements: No fish is a bird. All birds are animals. Conclusions: I. No fish is an animal. II. Some animals are not fish.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: B. Only conclusion II is true

    Birds are animals and no bird is a fish, so some animals (the birds) are not fish. Fish could still be animals, so I does not follow.

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20. 19

    Statements: All engineers are graduates. All graduates are literate. Conclusions: I. All engineers are literate. II. Some literate people are engineers.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: E. Both I and II are true

    Engineers lie inside graduates, which lie inside literate people, so all engineers are literate and some literate people are engineers.

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21. 20

    Statements: Some phones are tablets. No tablet is a watch. Conclusions: I. Some phones are not watches. II. Some watches are phones.

    AOnly conclusion I is trueBOnly conclusion II is trueCEither I or II is trueDNeither I nor II is trueEBoth I and II are true

    Correct answer: A. Only conclusion I is true

    The phones that are tablets cannot be watches, so some phones are not watches. Whether any watch is a phone is not known.

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