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Logical Deduction

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Logical Deduction

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Sample Questions

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Sample Questions – Logical Deduction


The best way to master Logical Deduction is to practise different forms of propositions and learn how to determine whether a conclusion necessarily follows from the given premises.

The questions in this chapter cover the major patterns used in Logical Deduction, including proposition identification, A-E-I-O classification, distribution, conversion, obversion, contraposition, middle-term analysis, syllogism, and conclusion testing.

How to Use This Chapter

First try to solve each question yourself. Then compare your answer with the explanation. Focus not only on the correct option, but also on why the other conclusions do not follow.

Type 1: Identify the Proposition

Question 1

Statement: All doctors are graduates.

What type of proposition is this?

  1. A-Type
  2. E-Type
  3. I-Type
  4. O-Type

Answer: A-Type

Explanation: The statement has the form All S are P. It is universal and affirmative, so it is an A proposition.

Question 2

Statement: No engineers are artists.

Identify the proposition type.

  1. A-Type
  2. E-Type
  3. I-Type
  4. O-Type

Answer: E-Type

Explanation: The form is No S are P. It is universal and negative, so it is an E proposition.

Question 3

Statement: Some students are athletes.

Identify the proposition type.

  1. A-Type
  2. E-Type
  3. I-Type
  4. O-Type

Answer: I-Type

Explanation: The form is Some S are P. It is particular and affirmative, so it is an I proposition.

Question 4

Statement: Some teachers are not writers.

Identify the proposition type.

  1. A-Type
  2. E-Type
  3. I-Type
  4. O-Type

Answer: O-Type

Explanation: The form is Some S are not P. It is particular and negative, so it is an O proposition.

Type 2: Identify Subject, Predicate and Copula

Question 5

Consider the statement:

All poets are writers.

Which of the following correctly identifies the four components?

  1. All = Subject, poets = Quantifier, are = Predicate, writers = Copula
  2. All = Quantifier, poets = Subject, are = Copula, writers = Predicate
  3. All = Copula, poets = Predicate, are = Quantifier, writers = Subject
  4. All = Predicate, poets = Subject, are = Quantifier, writers = Copula

Answer: B

Explanation: All is the quantifier, poets is the subject, are is the copula, and writers is the predicate.

Question 6

In the statement "No doctors are engineers", what is the predicate?

  1. No
  2. Doctors
  3. Are
  4. Engineers

Answer: D. Engineers

Explanation: The statement tells us something about doctors and excludes them from the class of engineers. Therefore, engineers is the predicate.

Type 3: Distribution of Terms

Question 7

In which proposition is only the subject distributed?

  1. A-Type
  2. E-Type
  3. I-Type
  4. O-Type

Answer: A-Type

Explanation: In an A proposition, All S are P, the subject is distributed while the predicate is not.

Question 8

Which proposition distributes both its subject and predicate?

  1. A-Type
  2. E-Type
  3. I-Type
  4. O-Type

Answer: B. E-Type

Explanation: In No S are P, both the subject and predicate are distributed.

Question 9

Which proposition distributes neither the subject nor the predicate?

  1. A-Type
  2. E-Type
  3. I-Type
  4. O-Type

Answer: C. I-Type

Explanation: In Some S are P, neither term refers to the entire class.

Question 10

In the proposition "Some students are not athletes", which term is distributed?

  1. Students only
  2. Athletes only
  3. Both students and athletes
  4. Neither students nor athletes

Answer: B. Athletes only

Explanation: The statement is O-type: Some S are not P. The subject is undistributed and the predicate is distributed.

Type 4: Conversion

Question 11

Which is the valid converse of the following statement?

No fish are whales.

  1. All whales are fish.
  2. Some whales are fish.
  3. No whales are fish.
  4. Some fish are not whales.

Answer: C. No whales are fish.

Explanation: An E-type proposition can be validly converted by interchanging the subject and predicate. Therefore, No fish are whales becomes No whales are fish.

Question 12

What is the valid converse of:

Some boys are poets.

  1. All poets are boys.
  2. No poets are boys.
  3. Some poets are boys.
  4. Some poets are not boys.

Answer: C. Some poets are boys.

Explanation: I-type propositions can be converted by interchanging the subject and predicate.

Question 13

Which of the following has no valid conversion?

  1. All S are P
  2. No S are P
  3. Some S are P
  4. Some S are not P

Answer: D. Some S are not P

Explanation: O-type propositions do not have a valid simple conversion in the standard framework.

Type 5: Obversion and Contraposition

Question 14

Which is the valid obverse of:

All birds are mammals.

  1. No birds are mammals.
  2. No birds are non-mammals.
  3. All non-birds are mammals.
  4. Some birds are non-mammals.

Answer: B. No birds are non-mammals.

Explanation: In obversion, the quality changes and the predicate is replaced by its complement.

Question 15

Which is the valid obverse of:

No poets are singers.

  1. All poets are non-singers.
  2. Some poets are non-singers.
  3. No non-poets are singers.
  4. All singers are poets.

Answer: A. All poets are non-singers.

Explanation: The E-type proposition becomes an A-type proposition with the predicate replaced by its complement.

Question 16

What is the valid contrapositive of:

All birds are mammals.

  1. All mammals are birds.
  2. All non-mammals are non-birds.
  3. No birds are mammals.
  4. Some non-mammals are birds.

Answer: B. All non-mammals are non-birds.

Explanation: The subject and predicate are interchanged and both are replaced by their complements.

Type 6: Identify the Middle Term

Question 17

Consider the following premises:

All doctors are educated.

All educated people are skilled.

What is the middle term?

  1. Doctors
  2. Educated people
  3. Skilled people
  4. Doctors and skilled people

Answer: B. Educated people

Explanation: The term educated people appears in both premises and connects doctors with skilled people.

Question 18

Consider:

All dogs are animals.

All tigers are dogs.

Which term is the middle term?

  1. Tigers
  2. Animals
  3. Dogs
  4. Animals and tigers

Answer: C. Dogs

Explanation: Dogs appears in both premises and connects tigers with animals.

Type 7: Simple Syllogism

Question 19

Read the following statements:

1. All lotus are flowers.

2. All flowers are beautiful.

Conclusion: All lotus are beautiful.

  1. Conclusion follows
  2. Conclusion does not follow
  3. Both are contradictory
  4. Cannot be determined because there is no middle term

Answer: A. Conclusion follows

Explanation: The chain is Lotus → Flowers → Beautiful. The middle term is flowers, and the conclusion connects lotus with beautiful.

Question 20

Consider:

1. All teachers are educated.

2. All educated people are knowledgeable.

Which conclusion follows?

  1. All knowledgeable people are teachers.
  2. Some knowledgeable people are not teachers.
  3. All teachers are knowledgeable.
  4. No teachers are knowledgeable.

Answer: C. All teachers are knowledgeable.

Explanation: Teachers are included in educated people, and educated people are included in knowledgeable people. Therefore, teachers are included in knowledgeable people.

Type 8: No Definite Conclusion

Question 21

Consider:

1. All birds are animals.

2. All fishes are animals.

Which conclusion follows?

  1. All birds are fishes.
  2. Some birds are fishes.
  3. No birds are fishes.
  4. No definite conclusion follows.

Answer: D. No definite conclusion follows.

Explanation: Both birds and fishes are related to animals, but no definite relationship between birds and fishes is established.

Question 22

Consider:

1. All puppets are dolls.

2. Some dolls are rattles.

Which conclusion can definitely be drawn?

  1. Some puppets are rattles.
  2. All rattles are puppets.
  3. Some rattles are dolls.
  4. All dolls are puppets.

Answer: C. Some rattles are dolls.

Explanation: This is the valid conversion of the particular affirmative statement Some dolls are rattles.

Type 9: Particular Premise

Question 23

Consider:

1. Some writers are players.

2. All players are musicians.

Which conclusion follows?

  1. All writers are musicians.
  2. Some writers are musicians.
  3. All musicians are writers.
  4. No writers are musicians.

Answer: B. Some writers are musicians.

Explanation: Some writers are players, and all players are musicians. Therefore, those writers who are players must also be musicians.

Question 24

Consider:

1. Some boys are thieves.

2. All thieves are dacoits.

Which conclusion follows?

  1. All dacoits are boys.
  2. Some boys are dacoits.
  3. All boys are dacoits.
  4. No boys are dacoits.

Answer: B. Some boys are dacoits.

Explanation: The particular premise tells us that at least one boy is a thief. Since every thief is a dacoit, that boy is also a dacoit.

Type 10: Negative Premise

Question 25

Consider:

1. All grasses are trees.

2. No trees are shrubs.

Which conclusion follows?

  1. All grasses are shrubs.
  2. Some grasses are shrubs.
  3. No grasses are shrubs.
  4. All shrubs are grasses.

Answer: C. No grasses are shrubs.

Explanation: Grasses are included in trees, while trees are completely excluded from shrubs. Therefore, grasses cannot belong to shrubs.

Question 26

Consider:

1. All cakes are candies.

2. No candy is pastry.

Which conclusion follows?

  1. All cakes are pastry.
  2. No cakes are pastry.
  3. Some cakes are pastry.
  4. All pastry are cakes.

Answer: B. No cakes are pastry.

Explanation: Cakes are contained within candies, and candies have no overlap with pastry. Therefore, cakes also have no overlap with pastry.

Type 11: Both Premises Particular

Question 27

Consider:

1. Some books are pens.

2. Some pens are erasers.

Which conclusion follows?

  1. All books are erasers.
  2. Some books are erasers.
  3. Some erasers are books.
  4. No definite conclusion follows.

Answer: D. No definite conclusion follows.

Explanation: Both premises are particular. The pens mentioned in the two statements need not refer to the same members. Therefore, no definite relationship between books and erasers can be established.

Type 12: Both Premises Negative

Question 28

Consider:

1. No flowers are mangoes.

2. No mangoes are cherries.

Which conclusion follows?

  1. No flowers are cherries.
  2. Some flowers are cherries.
  3. All flowers are cherries.
  4. No definite conclusion follows.

Answer: D. No definite conclusion follows.

Explanation: The premises establish that flowers do not overlap with mangoes and mangoes do not overlap with cherries. They do not establish a definite relationship between flowers and cherries.

Type 13: Middle Term Not Distributed

Question 29

Consider:

1. All fans are watches.

2. Some watches are black.

What is the correct conclusion?

  1. All fans are black.
  2. Some fans are black.
  3. All black objects are fans.
  4. No definite mediate conclusion follows.

Answer: D. No definite mediate conclusion follows.

Explanation: The middle term is watches. It is not distributed in either premise. Therefore, no definite mediate conclusion can be drawn.

Type 14: Identify the Valid Conclusion

Question 30

Statements:

1. All buses are vans.

2. Some cycles are vans.

Which of the following is definitely true?

  1. Some buses are cycles.
  2. All cycles are buses.
  3. Some vans are cycles.
  4. All vans are buses.

Answer: C. Some vans are cycles.

Explanation: The second premise says Some cycles are vans. Its valid converse is Some vans are cycles.

Type 15: Complete Syllogism Analysis

Question 31

Statements:

1. All men are boys.

2. All boys are students.

Which conclusion follows?

  1. All students are boys.
  2. All men are students.
  3. Some students are not boys.
  4. No men are students.

Answer: B. All men are students.

Explanation: The logical chain is Men → Boys → Students. Therefore, all men are students.

Question 32

Statements:

1. Some lamps are candles.

2. No candles are bulbs.

Which conclusion follows?

  1. Some lamps are bulbs.
  2. Some lamps are not bulbs.
  3. All lamps are bulbs.
  4. No lamps are candles.

Answer: B. Some lamps are not bulbs.

Explanation: Some lamps are candles, and no candle is a bulb. Therefore, those lamps that are candles are not bulbs.

Type 16: Find the Incorrect Conclusion

Question 33

Statements:

1. All engineers are graduates.

2. All graduates are educated.

Which conclusion does NOT follow?

  1. All engineers are educated.
  2. Some educated people are graduates, under the traditional syllogistic treatment.
  3. All graduates are engineers.
  4. Engineers are included within educated people.

Answer: C. All graduates are engineers.

Explanation: The premises establish Engineers → Graduates → Educated. They do not establish the reverse relationship Graduates → Engineers.

Type 17: Multiple Conclusions

Question 34

Statements:

1. All teachers are educated.

2. All educated people are knowledgeable.

Conclusions:

I. All teachers are knowledgeable.

II. All knowledgeable people are teachers.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions follow
  4. Neither conclusion follows

Answer: A. Only conclusion I follows

Explanation: The chain Teachers → Educated → Knowledgeable establishes conclusion I. The reverse relationship is not established, so conclusion II does not follow.

Question 35

Statements:

1. All cakes are candies.

2. No candy is pastry.

Conclusions:

I. No cakes are pastry.

II. No pastry is cake.

  1. Only conclusion I follows
  2. Only conclusion II follows
  3. Both conclusions follow
  4. Neither conclusion follows

Answer: C. Both conclusions follow

Explanation: Cakes are excluded from pastry through the chain Cakes → Candies → not Pastry. The E-type relationship can also be converted, giving No pastry is cake.

Type 18: Find the Middle Term and Conclusion

Question 36

Statements:

1. All artists are creative.

2. All creative people are imaginative.

Which combination is correct?

  1. Middle term = Artists; Conclusion = All creative people are artists
  2. Middle term = Creative people; Conclusion = All artists are imaginative
  3. Middle term = Imaginative people; Conclusion = All creative people are artists
  4. Middle term = Artists; Conclusion = All imaginative people are artists

Answer: B

Explanation: Creative people occur in both premises and act as the middle term. The resulting relationship is Artists → Creative → Imaginative, so all artists are imaginative.

Type 19: Apply the Complete Logical Framework

Question 37

Statements:

1. All doctors are graduates.

2. No graduates are uneducated.

Which conclusion follows?

  1. All doctors are uneducated.
  2. No doctors are uneducated.
  3. Some doctors are uneducated.
  4. All uneducated people are doctors.

Answer: B. No doctors are uneducated.

Explanation: Doctors are included in graduates, and graduates are completely excluded from uneducated people. Therefore, doctors are also excluded from uneducated people.

Question 38

Statements:

1. Some musicians are teachers.

2. All teachers are educated.

Which conclusion follows?

  1. All musicians are educated.
  2. Some musicians are educated.
  3. All educated people are musicians.
  4. No musicians are educated.

Answer: B. Some musicians are educated.

Explanation: Some musicians are teachers, and all teachers are educated. Therefore, at least some musicians are educated.

Type 20: Advanced Mixed Questions

Question 39

Statements:

1. All managers are graduates.

2. Some graduates are writers.

Which conclusion is definitely established?

  1. Some managers are writers.
  2. All writers are managers.
  3. Some writers are graduates.
  4. All graduates are managers.

Answer: C. Some writers are graduates.

Explanation: The second premise itself establishes that some graduates are writers. Its valid conversion is Some writers are graduates. We cannot conclude that the writers mentioned are managers.

Question 40

Statements:

1. No poets are singers.

2. Some writers are poets.

Which conclusion follows?

  1. Some writers are not singers.
  2. All writers are singers.
  3. Some singers are writers.
  4. All poets are writers.

Answer: A. Some writers are not singers.

Explanation: Some writers are poets, and no poets are singers. Therefore, those writers who are poets are not singers.

Type 21: Concept-Based Questions

Question 41

Which of the following is the most important requirement for deriving a definite conclusion in a standard two-premise syllogism?

  1. The conclusion must contain the middle term.
  2. The middle term must be distributed at least once.
  3. Both premises must always be particular.
  4. The conclusion must always be negative.

Answer: B. The middle term must be distributed at least once.

Explanation: If the middle term is not distributed in either premise, it cannot adequately connect the major and minor terms for a definite syllogistic conclusion.

Question 42

Which statement about the conclusion of a standard syllogism is correct?

  1. It must contain the middle term.
  2. It can introduce a completely new term.
  3. It should contain the major and minor terms.
  4. It must always be universal.

Answer: C. It should contain the major and minor terms.

Explanation: The middle term connects the premises but does not form part of the standard conclusion.

Question 43

If one premise is negative, what must be true of a valid conclusion?

  1. The conclusion must be affirmative.
  2. The conclusion must be negative.
  3. The conclusion must be universal.
  4. The conclusion must contain the middle term.

Answer: B. The conclusion must be negative.

Explanation: A negative premise requires a negative conclusion in the standard syllogistic framework.

Question 44

If one premise is particular, what should you expect regarding the quantity of a valid conclusion?

  1. It must be universal.
  2. It must be particular.
  3. It must contain the middle term.
  4. It must be negative.

Answer: B. It must be particular.

Explanation: A particular premise does not provide sufficient basis for a universal conclusion.

Type 22: Statement and Conclusion Practice

Question 45

Statements:

1. All nurses are doctors.

2. Some doctors are musicians.

Conclusions:

I. Some nurses are musicians.

II. Some musicians are doctors.

  1. Only I follows
  2. Only II follows
  3. Both I and II follow
  4. Neither I nor II follows

Answer: B. Only II follows

Explanation: The second premise directly gives Some doctors are musicians, whose converse is Some musicians are doctors. The premises do not establish that the doctors who are musicians are nurses.

Question 46

Statements:

1. All artists are creative.

2. No creative person is careless.

Conclusions:

I. No artists are careless.

II. Some careless people are artists.

  1. Only I follows
  2. Only II follows
  3. Both follow
  4. Neither follows

Answer: A. Only I follows

Explanation: Artists are creative, and creative people are excluded from careless people. Therefore, no artists are careless. Conclusion II contradicts the established relationship.

Type 23: Find the Definite Inference

Question 47

Statements:

1. Some teachers are writers.

2. All writers are readers.

Which conclusion definitely follows?

  1. All teachers are readers.
  2. Some teachers are readers.
  3. All readers are teachers.
  4. No teachers are readers.

Answer: B. Some teachers are readers.

Explanation: Some teachers are writers, and every writer is a reader. Therefore, those teachers who are writers are also readers.

Question 48

Statements:

1. No athletes are musicians.

2. Some students are athletes.

Which conclusion follows?

  1. Some students are not musicians.
  2. All students are musicians.
  3. Some musicians are students.
  4. No students are athletes.

Answer: A. Some students are not musicians.

Explanation: Some students are athletes, while no athlete is a musician. Therefore, those students who are athletes are not musicians.

Type 24: Advanced Syllogistic Reasoning

Question 49

Statements:

1. All managers are graduates.

2. No graduates are uneducated.

Conclusions:

I. No managers are uneducated.

II. No uneducated people are managers.

  1. Only I follows
  2. Only II follows
  3. Both I and II follow
  4. Neither follows

Answer: C. Both I and II follow

Explanation: Managers are included in graduates, and graduates are completely excluded from uneducated people. Therefore, no managers are uneducated. The same E-type relationship can be expressed in reverse as No uneducated people are managers.

Question 50

Statements:

1. All poets are writers.

2. Some writers are teachers.

Conclusions:

I. Some poets are teachers.

II. Some teachers are writers.

III. All poets are writers.

  1. Only I follows
  2. Only II and III follow
  3. Only I and III follow
  4. All follow

Answer: B. Only II and III follow

Explanation: Conclusion III is directly given by the first premise. Conclusion II is the valid converse of Some writers are teachers. However, the premises do not establish that the writers who are teachers are poets, so conclusion I does not follow.

Quick Answer Key

Question Answer Main Concept
1AA-Type Proposition
2BE-Type Proposition
3CI-Type Proposition
4DO-Type Proposition
5BProposition Components
6DPredicate
7ADistribution
8BDistribution
9CDistribution
10BO-Type Distribution
11CConversion
12CConversion
13DConversion
14BObversion
15AObversion
16BContraposition
17BMiddle Term
18CMiddle Term
19ASyllogism
20CSyllogism
21DNo Definite Conclusion
22CParticular Inference
23BParticular Premise
24BParticular Premise
25CNegative Premise
26BNegative Premise
27DBoth Particular
28DBoth Negative
29DMiddle-Term Distribution
30CConversion
31BChain Reasoning
32BNegative Premise
33CDirection of Relationship
34AMultiple Conclusions
35CUniversal Negative
36BMiddle Term
37BChain + Negative
38BParticular Inference
39CConversion
40ANegative Relationship
41BMiddle-Term Rule
42CTerms of Conclusion
43BNegative Conclusion
44BParticular Conclusion
45BMultiple Conclusions
46ANegative Syllogism
47BParticular Chain
48ANegative Relationship
49CAdvanced Syllogism
50BAdvanced Multiple Conclusions

Common Traps in Logical Deduction Questions

Trap 1: Reversing an "All" Statement

All A are B does not mean All B are A.

Trap 2: Treating "Some" as "All"

Some A are B does not mean All A are B.

Trap 3: Joining Unconnected Classes

If two classes are both related to a third class, that does not automatically establish a relationship between them.

Trap 4: Ignoring the Middle Term

If the middle term is not distributed in either premise, a definite mediate conclusion cannot be obtained.

Trap 5: Confusing Possibility with Necessity

A conclusion may be possible without necessarily following. Logical Deduction asks what must follow.

Fast Solving Strategy

For examination purposes, use the following sequence when solving a Logical Deduction question:

1. Identify the Quantifier
↓
2. Classify A / E / I / O
↓
3. Find S, P and M
↓
4. Check Distribution
↓
5. Connect the Premises
↓
6. Check Quantity and Quality
↓
7. Test the Conclusion
↓
8. Select Only What Necessarily Follows

Practice Challenge

Try solving the following questions without looking at the answers. These combine several techniques discussed in this chapter.

Challenge 1

All researchers are graduates.

Some graduates are writers.

Which conclusion definitely follows?

  1. Some researchers are writers.
  2. Some writers are graduates.
  3. All writers are researchers.
  4. All graduates are researchers.

Answer: B. Some writers are graduates.

Challenge 2

No engineers are artists.

Some designers are engineers.

Which conclusion follows?

  1. Some designers are not artists.
  2. All designers are artists.
  3. Some artists are designers.
  4. All engineers are designers.

Answer: A. Some designers are not artists.

Challenge 3

All musicians are artists.

No artists are careless.

Which conclusion follows?

  1. No musicians are careless.
  2. Some musicians are careless.
  3. All careless people are musicians.
  4. Some artists are musicians.

Answer: A. No musicians are careless.

Final Takeaway

The most effective way to solve Logical Deduction questions is to convert statements into their logical structure, identify the A-E-I-O type, understand distribution, identify the middle term, connect the premises, and then test whether the conclusion necessarily follows.

Identify → Classify → Distribute → Connect → Deduce → Verify

With regular practice, these steps become automatic, allowing you to solve even complex syllogism and Logical Deduction questions quickly and accurately in competitive examinations.

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