Syllogism questions with answers and concepts

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142 practice questionsPage updated 27 Mar 2026Review metadata pendingPractice questions

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Syllogism is a form of logical reasoning where conclusions are drawn from two or more premises (statements). It is a fundamental topic in logical reasoning tests, requiring you to determine whether a given conclusion logically follows from the provided statements. Understanding the relationships between categorical statements is essential for solving these problems accurately.

Key concepts

Types of Categorical Statements

There are four standard types of categorical statements:

1. Universal Affirmative (A-type): All A are B
- Every member of set A is also a member of set B
- Example: All dogs are animals

2. Universal Negative (E-type): No A are B
- No member of set A is a member of set B
- Example: No fish are mammals

3. Particular Affirmative (I-type): Some A are B
- At least one member of set A is a member of set B
- Example: Some students are toppers

4. Particular Negative (O-type): Some A are not B
- At least one member of set A is not a member of set B
- Example: Some fruits are not sweet

Venn Diagram Representation

Venn diagrams provide an unambiguous geometric proof method for categorical syllogisms:

1. Universal Affirmative: 'All A are B' ( $A \subseteq B$ )

+-----------------------+
|  Set B                |
|      +---------+      |
|      |  Set A  |      |
|      +---------+      |
+-----------------------+

Circle A is completely enclosed inside Circle B.

2. Universal Negative: 'No A are B' ( $A \cap B = \emptyset$ )

+---------+       +---------+
|  Set A  |       |  Set B  |
+---------+       +---------+

Circles A and B are completely disjoint with zero overlap.

3. Particular Affirmative: 'Some A are B' ( $A \cap B \neq = \emptyset$ )

+---------+
|  Set A  |---+
|      [A ∩ B]|  Set B  |
+---------+   +---------+

Circles A and B share an overlapping intersection containing at least one member.

4. Particular Negative: 'Some A are not B' ( $A ∖ B \neq = \emptyset$ )

+---------+
| [A \ B] |---+
|      (A ∩ B)|  Set B  |
+---------+   +---------+

The region of Circle A that lies strictly outside Circle B is non-empty.

Always draw the minimal constraint diagram based strictly on what the premises force, then verify if a conclusion holds across every possible valid configuration.

Immediate Inferences (Conversion)

Conversion is drawing a valid conclusion by interchanging the subject and predicate:

'All A are B' -> 'Some B are A' (valid)
'No A are B' -> 'No B are A' (valid)
'Some A are B' -> 'Some B are A' (valid)
'Some A are not B' -> No valid conversion

Note: 'All A are B' cannot be converted to 'All B are A' - this would be the fallacy of illicit conversion.

Distribution of Terms

A term is 'distributed' when the statement makes an assertion about every member of that class:

'All A are B': A is distributed, B is undistributed
'No A are B': Both A and B are distributed
'Some A are B': Neither A nor B is distributed
'Some A are not B': A is undistributed, B is distributed

Rules for valid syllogisms:
1. The middle term must be distributed at least once
2. If a term is distributed in the conclusion, it must be distributed in the premise

Syllogism Rules and Fallacies

Key rules for valid syllogistic reasoning:

1. Two negative premises cannot yield a valid conclusion
2. Two particular premises cannot yield a valid universal conclusion
3. If one premise is negative, the conclusion must be negative
4. If one premise is particular, the conclusion must be particular
5. The middle term must be distributed at least once

Exam Conventions vs. Modern Logic:
- Traditional / Competitive Exam Convention (TCS, SSC, Banking): Universal statements ('All A are B') are understood with existential import (the class A exists and is non-empty), making 'Some B are A' a valid subaltern inference.
- Modern Predicate Logic Convention: Universal statements do not imply that instances exist. Thus 'All A are B' does not entail 'Some B are A' unless an explicit existence premise is provided (avoiding the existential fallacy).

Common fallacies to avoid:
Illicit major/minor: Distributing a term in conclusion not distributed in premise
Undistributed middle: Middle term not distributed in either premise
Affirmative conclusion from negative premise
Existential fallacy: Inferring a particular conclusion from universal premises without existence

Three-Statement and Multi-Premise Syllogisms

For problems with three or more statements:

1. Identify all distinct terms (usually 3 or more categories)
2. Find the common term that links statements
3. Chain the relationships step by step
4. Draw a comprehensive Venn diagram
5. Check each conclusion against all valid diagram possibilities

With possibility cases (when answer choices include 'possibly true'):
'Definitely true' = True in all valid diagrams
'Definitely false' = False in all valid diagrams
'Possibly true' = True in at least one valid diagram
'Possibly false' = False in at least one valid diagram
'Cannot say' = Neither definitely true nor definitely false

Check the idea while it is fresh.Open a focused exercise without losing this article.Practise this concept

Worked examples

Example 1

Statements:
1. All pens are books
2. All books are boxes

Conclusions:
I. All pens are boxes
II. Some boxes are pens

Solution

Step 1: Draw the Venn diagram based on statements.
- 'All pens are books' -> Circle P inside Circle B
- 'All books are boxes' -> Circle B inside Circle BX

Step 2: This creates: Circle P (pens) inside Circle B (books) inside Circle BX (boxes)

Step 3: Check Conclusion I: 'All pens are boxes'
Since all pens are books and all books are boxes, all pens must be boxes. CONCLUSION I FOLLOWS.

Step 4: Check Conclusion II: 'Some boxes are pens'
Since all pens are boxes (subset relationship), at least some boxes (those that are pens) are indeed pens. CONCLUSION II FOLLOWS.

Answer: Both I and II follow

Example 2

Statements:
1. Some cats are dogs
2. No dog is a cow

Conclusions:
I. No cat is a cow
II. Some cats are not cows

Solution

Step 1: Draw Venn diagram.
- 'Some cats are dogs' -> Circles C and D overlap
- 'No dog is a cow' -> Circle D and Circle CW are separate

Step 2: Check Conclusion I: 'No cat is a cow'
The overlapping region between cats and dogs has no connection to cows. However, cats that are NOT dogs could potentially be cows. So this is NOT DEFINITELY TRUE. CONCLUSION I DOES NOT FOLLOW.

Step 3: Check Conclusion II: 'Some cats are not cows'
The cats that are dogs (overlap region) are definitely not cows (since no dog is a cow). Therefore, some cats (at least those that are dogs) are not cows. CONCLUSION II FOLLOWS.

Answer: Only II follows

Example 3

Statements:
1. All mountains are hills
2. Some hills are rivers
3. All rivers are lakes

Conclusions:
I. Some mountains are lakes
II. Some hills are lakes
III. No mountain is a lake

Solution

Step 1: Draw comprehensive Venn diagram:
- M (mountains) inside H (hills)
- H overlaps with R (rivers)
- R inside L (lakes)

Step 2: Check Conclusion I: 'Some mountains are lakes'
Mountains are inside hills. Some hills are rivers (which are inside lakes). But the hills that are rivers may or may not include mountains. Thus Conclusion I is possible, but does not definitely follow on its own.

Step 3: Check Conclusion II: 'Some hills are lakes'
Some hills are rivers, and all rivers are lakes. Therefore, those hills that are rivers must also be lakes. CONCLUSION II DEFINITELY FOLLOWS.

Step 4: Check Conclusion III: 'No mountain is a lake'
Same reasoning as I - mountains could overlap with lakes, or be completely disjoint. Thus Conclusion III does not definitely follow on its own.

Step 5: Check for Complementary Pair (Either/Or):
Conclusions I ('Some mountains are lakes' - I-type) and III ('No mountain is a lake' - E-type) share the same subject and predicate. One affirmative and one negative covering all possibilities form a complementary pair: either some mountains are lakes, or no mountain is a lake.

Answer: Only II and either I or III follow (or 'Only II follows' if choices evaluate independent definite conclusions without an either/or option).

Example 4

Statements:
1. No table is a chair
2. Some chairs are stools
3. All stools are desks

Conclusions:
I. Some desks are not tables
II. Some stools are not tables
III. All desks are tables

Solution

Step 1: Draw Venn diagram:
- T (tables) and C (chairs) are separate
- C overlaps with S (stools)
- S inside D (desks)

Step 2: Check Conclusion I: 'Some desks are not tables'
The stools that are chairs are inside desks. Since chairs are not tables, and these stools (which are chairs) are inside desks, some desks (at least those containing stool-chairs) are not tables. CONCLUSION I FOLLOWS.

Step 3: Check Conclusion II: 'Some stools are not tables'
Some stools are chairs, and no chair is a table. Therefore, those stools that are chairs are definitely not tables. CONCLUSION II FOLLOWS.

Step 4: Check Conclusion III: 'All desks are tables'
This contradicts Conclusion I which we've proven true. Also, desks contain stools which contain chairs which are not tables. CONCLUSION III DOES NOT FOLLOW.

Answer: Both I and II follow

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

Interpret 'Either I or II follows' to mean exactly one conclusion follows.

Statements:
No chair is table.
Some tables are desks.

Conclusions:
I. No desk is chair.
II. Some desks are chairs.

Which conclusion(s) follow?

Only I follows
Only II follows
Either I or II follows
Neither I nor II follows

Answer: D. Neither I nor II follows

Explanation

The premises guarantee some desks that are tables, and none of those desks is a chair. If no desk is a chair, I follows; if any desk is a chair, II follows. Under the stated exactly-one convention, one of I or II must follow, so 'Either I or II follows' is the answer.

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

Use modern predicate logic: universal statements do not imply that a class exists.

Statements:
All politicians are corrupt.
Some corrupt are caught.

Conclusions:
I. Some politicians are caught.
II. Some corrupt are politicians.

Which conclusion(s) follow?

Only I follows
Only II follows
Both I and II follow
Neither I nor II follows

Answer: D. Neither I nor II follows

Explanation

The caught corrupt people are not necessarily politicians, so I does not follow. 'All politicians are corrupt' does not establish that any politicians exist, so II does not follow either. Neither conclusion follows.

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

Statements:
All teachers are educated.
Some educated are women.
All women are kind.

Conclusions:
I. Some teachers are women.
II. Some educated are kind.

Which conclusion(s) follow?

Only I follows
Only II follows
Both I and II follow
Neither I nor II follows

Answer: B. Only II follows

Explanation

Step 1: Draw Venn diagram - Teachers Educated, Educated intersect Women != , Women Kind
Step 2: Some educated are women and all women are kind -> Some educated are kind (II follows)
Step 3: The women among educated may or may not be teachers
Step 4: I cannot be concluded
Answer: Only II follows

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Always draw Venn diagrams for syllogism problems - visual representation prevents logical errors
Remember: 'Some A are B' only guarantees at least one A is B, not that some A are NOT B
When checking conclusions, ask: 'Is this true in ALL valid diagram configurations?' If yes, it follows; if no, it doesn't
For 'All A are B' statements, never assume 'All B are A' - this is the most common error
If the conclusion is universal (All/No), both premises typically need to be universal too
Practice identifying the middle term quickly - it's the term that appears in both premises but not in the conclusion
With three or more statements, chain them logically: connect statements through common terms
When answer choices include 'Either I or II follows', check if the conclusions are complementary (one affirmative, one negative about the same terms)

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Next topic: Data Sufficiency

Syllogism questions with answers and concepts

Learn syllogism with concept notes and worked examples, then practise focused questions with explained answers. Build accuracy for placement and competitive aptitude tests before trying timed mode.

142 practice questionsPage updated 27 Mar 2026Review metadata pendingPractice questions

Practise this concept

Key concepts

Types of Categorical Statements

There are four standard types of categorical statements:

1. Universal Affirmative (A-type): All A are B
- Every member of set A is also a member of set B
- Example: All dogs are animals

2. Universal Negative (E-type): No A are B
- No member of set A is a member of set B
- Example: No fish are mammals

3. Particular Affirmative (I-type): Some A are B
- At least one member of set A is a member of set B
- Example: Some students are toppers

4. Particular Negative (O-type): Some A are not B
- At least one member of set A is not a member of set B
- Example: Some fruits are not sweet

Venn Diagram Representation

Venn diagrams provide an unambiguous geometric proof method for categorical syllogisms:

1. Universal Affirmative: 'All A are B' ( $A \subseteq B$ )

+-----------------------+
|  Set B                |
|      +---------+      |
|      |  Set A  |      |
|      +---------+      |
+-----------------------+

Circle A is completely enclosed inside Circle B.

2. Universal Negative: 'No A are B' ( $A \cap B = \emptyset$ )

+---------+       +---------+
|  Set A  |       |  Set B  |
+---------+       +---------+

Circles A and B are completely disjoint with zero overlap.

3. Particular Affirmative: 'Some A are B' ( $A \cap B \neq = \emptyset$ )

+---------+
|  Set A  |---+
|      [A ∩ B]|  Set B  |
+---------+   +---------+

Circles A and B share an overlapping intersection containing at least one member.

4. Particular Negative: 'Some A are not B' ( $A ∖ B \neq = \emptyset$ )

+---------+
| [A \ B] |---+
|      (A ∩ B)|  Set B  |
+---------+   +---------+

The region of Circle A that lies strictly outside Circle B is non-empty.

Always draw the minimal constraint diagram based strictly on what the premises force, then verify if a conclusion holds across every possible valid configuration.

Immediate Inferences (Conversion)

Conversion is drawing a valid conclusion by interchanging the subject and predicate:

'All A are B' -> 'Some B are A' (valid)
'No A are B' -> 'No B are A' (valid)
'Some A are B' -> 'Some B are A' (valid)
'Some A are not B' -> No valid conversion

Note: 'All A are B' cannot be converted to 'All B are A' - this would be the fallacy of illicit conversion.

Distribution of Terms

A term is 'distributed' when the statement makes an assertion about every member of that class:

'All A are B': A is distributed, B is undistributed
'No A are B': Both A and B are distributed
'Some A are B': Neither A nor B is distributed
'Some A are not B': A is undistributed, B is distributed

Rules for valid syllogisms:
1. The middle term must be distributed at least once
2. If a term is distributed in the conclusion, it must be distributed in the premise

Syllogism Rules and Fallacies

Key rules for valid syllogistic reasoning:

Three-Statement and Multi-Premise Syllogisms

For problems with three or more statements:

Check the idea while it is fresh.Open a focused exercise without losing this article.Practise this concept

Worked examples

Example 1

Statements:
1. All pens are books
2. All books are boxes

Conclusions:
I. All pens are boxes
II. Some boxes are pens

Solution

Step 1: Draw the Venn diagram based on statements.
- 'All pens are books' -> Circle P inside Circle B
- 'All books are boxes' -> Circle B inside Circle BX

Step 2: This creates: Circle P (pens) inside Circle B (books) inside Circle BX (boxes)

Step 3: Check Conclusion I: 'All pens are boxes'
Since all pens are books and all books are boxes, all pens must be boxes. CONCLUSION I FOLLOWS.

Step 4: Check Conclusion II: 'Some boxes are pens'
Since all pens are boxes (subset relationship), at least some boxes (those that are pens) are indeed pens. CONCLUSION II FOLLOWS.

Answer: Both I and II follow

Example 2

Statements:
1. Some cats are dogs
2. No dog is a cow

Conclusions:
I. No cat is a cow
II. Some cats are not cows

Solution

Step 1: Draw Venn diagram.
- 'Some cats are dogs' -> Circles C and D overlap
- 'No dog is a cow' -> Circle D and Circle CW are separate

Answer: Only II follows

Example 3

Statements:
1. All mountains are hills
2. Some hills are rivers
3. All rivers are lakes

Conclusions:
I. Some mountains are lakes
II. Some hills are lakes
III. No mountain is a lake

Solution

Step 1: Draw comprehensive Venn diagram:
- M (mountains) inside H (hills)
- H overlaps with R (rivers)
- R inside L (lakes)

Step 3: Check Conclusion II: 'Some hills are lakes'
Some hills are rivers, and all rivers are lakes. Therefore, those hills that are rivers must also be lakes. CONCLUSION II DEFINITELY FOLLOWS.

Step 4: Check Conclusion III: 'No mountain is a lake'
Same reasoning as I - mountains could overlap with lakes, or be completely disjoint. Thus Conclusion III does not definitely follow on its own.

Answer: Only II and either I or III follow (or 'Only II follows' if choices evaluate independent definite conclusions without an either/or option).

Example 4

Statements:
1. No table is a chair
2. Some chairs are stools
3. All stools are desks

Conclusions:
I. Some desks are not tables
II. Some stools are not tables
III. All desks are tables

Solution

Step 1: Draw Venn diagram:
- T (tables) and C (chairs) are separate
- C overlaps with S (stools)
- S inside D (desks)

Step 3: Check Conclusion II: 'Some stools are not tables'
Some stools are chairs, and no chair is a table. Therefore, those stools that are chairs are definitely not tables. CONCLUSION II FOLLOWS.

Answer: Both I and II follow

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

Interpret 'Either I or II follows' to mean exactly one conclusion follows.

Statements:
No chair is table.
Some tables are desks.

Conclusions:
I. No desk is chair.
II. Some desks are chairs.

Which conclusion(s) follow?

Only I follows
Only II follows
Either I or II follows
Neither I nor II follows

Answer: D. Neither I nor II follows

Explanation

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

Use modern predicate logic: universal statements do not imply that a class exists.

Statements:
All politicians are corrupt.
Some corrupt are caught.

Conclusions:
I. Some politicians are caught.
II. Some corrupt are politicians.

Which conclusion(s) follow?

Only I follows
Only II follows
Both I and II follow
Neither I nor II follows

Answer: D. Neither I nor II follows

Explanation

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

Statements:
All teachers are educated.
Some educated are women.
All women are kind.

Conclusions:
I. Some teachers are women.
II. Some educated are kind.

Which conclusion(s) follow?

Only I follows
Only II follows
Both I and II follow
Neither I nor II follows

Answer: B. Only II follows

Explanation

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Always draw Venn diagrams for syllogism problems - visual representation prevents logical errors
Remember: 'Some A are B' only guarantees at least one A is B, not that some A are NOT B
When checking conclusions, ask: 'Is this true in ALL valid diagram configurations?' If yes, it follows; if no, it doesn't
For 'All A are B' statements, never assume 'All B are A' - this is the most common error
If the conclusion is universal (All/No), both premises typically need to be universal too
Practice identifying the middle term quickly - it's the term that appears in both premises but not in the conclusion
With three or more statements, chain them logically: connect statements through common terms
When answer choices include 'Either I or II follows', check if the conclusions are complementary (one affirmative, one negative about the same terms)

Ready to test your understanding?

Work through 142 questions with explanations after each answer.

Start practice

Next topic: Data Sufficiency

Key concepts

Types of Categorical Statements

Venn Diagram Representation

Immediate Inferences (Conversion)

Distribution of Terms

Syllogism Rules and Fallacies

Three-Statement and Multi-Premise Syllogisms

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.

Key concepts

Types of Categorical Statements

Venn Diagram Representation

Immediate Inferences (Conversion)

Distribution of Terms

Syllogism Rules and Fallacies

Three-Statement and Multi-Premise Syllogisms

Worked examples

Example 1

Solution

Example 2

Solution

Example 3

Solution

Example 4

Solution

Representative solved questions

Question 1

Question 2

Question 3

Common mistakes and useful habits

Ready to test your understanding?

Keep building the same skill family.