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SYLLOGISM – Detailed Notes for CUET, CLAT & IPMAT

November 23, 2025 , , ,

 SYLLOGISM – Detailed Notes for CUET, CLAT & IPMAT

Syllogism is one of the most important topics in Logical Reasoning. You will find questions in CUET, CLAT, IPMAT, SSC, Banking and other competitive exams. This topic checks your ability to understand statements and draw logical conclusions.

Students often find Syllogism tricky. But with correct rules and simple techniques, you can solve every question correctly.

This article includes:

  • Meaning of syllogism
  • Types of statements
  • Types of conclusions
  • Venn diagram method
  • Shortcut rules
  • Special cases
  • Previous year questions
  • Practice questions

Let’s start.

SYLLOGISM – Detailed Notes for CUET, CLAT & IPMAT pdf

What is Syllogism?

Syllogism is a logical reasoning topic based on statements and conclusions.
The statements are always true.
You must judge whether the given conclusions logically follow the statements.

Syllogism uses three major keyword types:

  • All (Universal Positive)
  • No (Universal Negative)
  • Some (Particular Positive)
  • Some not (Particular Negative)

You must understand what each type means.

Type 1: Statements in Syllogism

1. Universal Positive (A-type)

Format: All A are B
Meaning: Every A lies inside B.
Venn Diagram: A completely inside B.

Examples:

  • All dogs are animals.
  • All books are papers.

2. Universal Negative (E-type)

Format: No A is B
Meaning: A and B never overlap.
Venn Diagram: A and B do not touch.

Examples:

  • No plant is an animal.
  • No circle is a square.

3. Particular Positive (I-type)

Format: Some A are B
Meaning: At least one A is B.

Examples:

  • Some students are athletes.
  • Some fruits are vitamins.

4. Particular Negative (O-type)

Format: Some A are not B
Meaning: At least one A is outside B.

Examples:

  • Some cars are not electric.
  • Some books are not novels.

Type 2: Valid Inferences / Conclusion Rules

These are the most important rules in Syllogism.
Memorize them.

Rule 1: A + A = A

All A are B
All B are C
Conclusion: “All A are C” follows.

Rule 2: E + A = E (Reverse only)

No A is B
All B are C
Conclusion: “No C is A” does not follow normally.
But “No A is C” also does NOT follow unless shown by a Venn diagram.

Always draw Venn for negatives.

Rule 3: A + I = I

All A are B
Some B are C
Conclusion: No definite conclusion.

This is a special trap.
Students often assume unnecessary connections.
Never assume.

Rule 4: I + I = No Conclusion

Some A are B
Some B are C
No definite conclusion.

Rule 5: Complementary Pairs

For either/or questions:

  • A conclusion with Some A are B
  • And the opposite Some A are not B

If both appear as options, you use the either–or rule.

Type 3: Venn Diagram Method

The Venn diagram is the safest method.
It gives 100% accuracy.

Steps:

  1. Read the first statement.
  2. Draw the Venn diagram correctly.
  3. Add the second statement.
  4. Draw the most general diagram possible.
  5. Test possible arrangements.
  6. Check conclusions.

Let’s see an example.

Example

Statements:

  1. All cats are animals.
  2. Some animals are wild.

Diagram:

  • Circle of Cats inside Animals.
  • Some part of Animals overlapping Wild.

Conclusion:

  • Some wild are animals → True (given)
  • Some cats are wild → Not definite
  • All animals are cats → False

Type 4: Standard Patterns

Below are classical patterns often asked in CUET, CLAT & IPMAT.

Pattern 1: All + All

Statements:
All A are B
All B are C

Conclusion:
All A are C → Valid
Some C are A → Valid (conversion)

Pattern 2: All + Some

Statements:
All A are B
Some B are C

Conclusion:
No definite conclusion between A and C.

Pattern 3: Some + Some

Statements:
Some A are B
Some B are C

Conclusion:
No definite conclusion.

Pattern 4: No + Some

Statements:
No A is B
Some B are C

Conclusion:
Some C are not A → Valid (following negative shading)

Pattern 5: No + All

Statements:
No A is B
All B are C

Conclusion:
No A is C → Valid
But No C is A? → Also valid (contrapositive)

Type 5: Conversion Rules

These are used in direct questions.

A-type (All A are B)

Conversion → Some B are A (possible)

E-type (No A is B)

Conversion → No B is A

I-type (Some A are B)

Conversion → Some B are A

O-type (Some A are not B)

Conversion → Not possible

Type 6: Possibility Questions

Possibility questions are very common in CUET & IPMAT.

Tip:

If the diagram does not restrict a situation, the possibility is true.

Example

Statements:
All A are B
Some B are C

Question: “Is it possible that all A are C?”

Answer: Yes, possible.
There is no restriction.

Type 7: Either–Or Cases

Either–Or is used only when:

  1. Both conclusions are individually false
  2. Both are complementary pairs
  3. Both involve the same terms

Complementary pairs:

  • Some A are B ↔ Some A are not B
  • All A are B ↔ Some A are not B
  • No A is B ↔ Some A are B

Common Mistakes Students Make

  • Assuming extra information
  • Thinking "possibility" is always true (it must not violate diagram)
  • Misunderstanding “some” (it means at least one)
  • Converting O-type statements incorrectly
  • Not checking reverse possibility diagrams

Type 8: Syllogism Previous Year Questions (PYQs)

Below are some previous year–based questions asked in CUET, CLAT, IPMAT and other exams.

PYQ 1 (CUET)

Statements:
All books are papers.
Some papers are notes.

Conclusions:

  1. Some notes are books.
  2. All notes are books.

Solution:
Draw Venn.
From diagram:
1 → Not definite
2 → False

Answer: Neither follows.

PYQ 2 (IPMAT)

Statements:
Some phones are smart.
All smart things are expensive.

Conclusions:

  1. Some phones are expensive.
  2. All expensive things are phones.

Solution:
1 → True (valid chain: Some A are B, All B are C → Some A are C)
2 → False

Answer: Only 1 follows.

PYQ 3 (CLAT)

Statements:
No student is lazy.
Some lazy people are artists.

Conclusions:

  1. Some artists are not students.
  2. All artists are students.

Solution:
“No student is lazy” → Students and Lazy separate
Some Lazy are Artists → Artists overlap Lazy
Therefore some artists lie in lazy circle.
Hence they cannot be students.

1 → True
2 → False

Answer: Only 1 follows.

PYQ 4 (CUET)

Statements:
All cars are vehicles.
No vehicle is cheap.

Conclusions:

  1. No car is cheap.
  2. All cheap are not vehicles.

Solution:
1 → True
2 → True (opposite of No vehicle is cheap)

Answer: Both follow.

Practice Questions (Created Based on PYQs)

Q1

Statements:
All trees are plants.
Some plants are herbs.

Conclusions:

  1. Some herbs are trees.
  2. Some plants are trees.

Answer:
1 → Not definite
2 → True

Q2

Statements:
Some boys are tall.
Some tall are athletes.

Conclusions:

  1. Some athletes are boys.
  2. No tall is boy.

Answer:
1 → Not definite
2 → False
Neither follows.

Q3

Statements:
No A is B.
Some B are C.

Conclusions:

  1. Some C are not A.
  2. Some A are C.

Answer:
1 → True
2 → False
Only 1 follows.

Q4

Statements:
All pens are blue.
No blue is plastic.

Conclusions:

  1. No pen is plastic.
  2. Some plastic are not pens.

Answer:
1 → True
2 → True

Q5

Statements:
Some laptops are tools.
All tools are devices.

Conclusions:

  1. Some laptops are devices.
  2. All laptops are devices.

Answer:
1 → True
2 → False

Syllogism Tricks for Exams (SEO Key Content)

These tricks help improve accuracy in CUET, CLAT & IPMAT reasoning.

✔ Trick 1: Always draw Venn for negative statements

“No A is B” type questions need diagrams.

✔ Trick 2: Don’t assume extra connections

Only use what is given.

✔ Trick 3: Chain method for positive statements

All A are B
All B are C
→ All A are C

✔ Trick 4: For possibility, check if diagram allows

If the basic diagram doesn’t stop it, it is possible.

✔ Trick 5: Learn complementary pairs

These help in “Either–Or” questions.

 

SYLLOGISM MCQs with Detailed Solutions

Q1.

Statements:
All A are B.
Some B are C.

Conclusions:

  1. Some C are A.
  2. All A are C.

a) Only 1 follows
b) Only 2 follows
c) Both follow
d) Neither follows

Answer: d) Neither follows

Explanation:
All A inside B.
Some B overlap C.
But A may or may not touch C.
Therefore no definite relation between A and C.
Hence none follow.

Q2.

Statements:
Some books are novels.
All novels are stories.

Conclusions:

  1. Some stories are books.
  2. All stories are books.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
Chain: Some books → novels → stories.
So some books become stories.
But not all stories are books.

Q3.

Statements:
All fruits are healthy.
No healthy thing is cheap.

Conclusions:

  1. No fruit is cheap.
  2. Some cheap are fruits.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
All fruits → healthy → not cheap.
So no fruit can be cheap.
Conclusion 2 is impossible.

Q4.

Statements:
Some boys are tall.
No tall person is weak.

Conclusions:

  1. Some boys are not weak.
  2. No boy is weak.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
Some boys are tall → tall are not weak → so some boys are not weak.
But we cannot say all boys are not weak.

Q5.

Statements:
All cats are animals.
Some animals are wild.

Conclusions:

  1. Some cats may be wild.
  2. Some wild are animals.

a) Only 1
b) Only 2
c) Both
d) None

Answer: c) Both

Explanation:
Some animals are wild → given.
Possible that cats sit in wild part because no restriction.
So both follow.

Q6.

Statements:
No A is B.
Some B are C.

Conclusions:

  1. Some C are not A.
  2. Some A are C.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
No A is B → B separate from A.
Some B are C → C overlaps B.
So that part of C cannot be A.
Thus some C are not A.

Q7.

Statements:
All pens are blue.
All blue are plastic.

Conclusions:

  1. All pens are plastic.
  2. Some plastic are pens.

a) Only 1
b) Only 2
c) Both
d) None

Answer: c) Both

Explanation:
Chain: pen → blue → plastic.
So both are valid.

Q8.

Statements:
Some flowers are red.
Some red are roses.

Conclusions:

  1. Some flowers are roses.
  2. Some roses are flowers.

a) Only 1
b) Only 2
c) Both
d) None

Answer: d) None

Explanation:
Overlap between flowers and red, red and roses exist.
But roses may lie in totally different part of red circle.
No definite overlap between flowers and roses.

Q9.

Statements:
All A are B.
All C are B.

Conclusions:

  1. Some B are A.
  2. A and C overlap.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
All A inside B → so some B are A.
But A and C may be separate inside B.

Q10.

Statements:
Some dogs are brown.
All brown are pets.

Conclusions:

  1. Some dogs are pets.
  2. All pets are brown.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
Chain: Some dogs → brown → pets.
So conclusion 1 is correct.
But not all pets must be brown.

Q11.

Statements:
Some A are B.
All B are C.

Conclusions:

  1. Some C are A.
  2. All C are A.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
Some A inside C because A → B → C.
But C may be bigger, so not all C are A.

Q12.

Statements:
No teacher is lazy.
Some lazy are young.

Conclusions:

  1. Some young are not teachers.
  2. All young are teachers.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
Lazy and teacher do not touch.
Some lazy are young → so some young lie in lazy.
Hence they cannot be teachers.

Q13.

Statements:
All books are papers.
Some papers are notes.

Conclusions:

  1. Some notes are books.
  2. Some papers are books.

a) Only 1
b) Only 2
c) Both
d) None

Answer: b) Only 2

Explanation:
All books are papers → so papers contain books.
But notes may overlap different part of papers; not sure if overlap books.

Q14.

Statements:
Some A are B.
Some B are C.
Some C are D.

Conclusion:

  1. A and C overlap.
  2. A and D overlap.

a) Only 1
b) Only 2
c) Both
d) None

Answer: d) None

Explanation:
Chain of “some” statements never gives definite conclusion.

Q15.

Statements:
All singers are artists.
Some artists are famous.

Conclusions:

  1. All famous are singers.
  2. Some singers may be famous.

a) Only 1
b) Only 2
c) Both
d) None

Answer: b) Only 2

Explanation:
Possibility exists that singers lie in famous part.
But famous could include non-singers too.

Q16.

Statements:
No student is doctor.
All doctors are rich.

Conclusions:

  1. No student is rich.
  2. Some rich are doctors.

a) Only 1
b) Only 2
c) Both
d) None

Answer: b) Only 2

Explanation:
Doctors and students are separate.
Doctors → rich.
So some rich are doctors.
But students may or may not be rich.

Q17.

Statements:
Some mobiles are smart.
No smart is cheap.

Conclusions:

  1. Some mobiles are not cheap.
  2. All mobiles are not cheap.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
Mobiles that are smart cannot be cheap.
But other mobiles may be cheap.

Q18.

Statements:
All chairs are wooden.
All tables are wooden.

Conclusions:

  1. Some wooden are chairs.
  2. Chairs and tables overlap.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
Wooden contains chairs.
But chairs and tables may be separate.

Q19.

Statements:
Some fruits are sweet.
All sweets are tasty.

Conclusions:

  1. Some fruits are tasty.
  2. All tasty things are fruits.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Q20.

Statements:
All toys are plastic.
Some plastic are green.

Conclusions:

  1. Some toys are green.
  2. All green are toys.

a) Only 1
b) Only 2
c) Both
d) None

Answer: d) None

Explanation:
Green part may overlap a different area of plastic.

Q21.

Statements:
Some pens are pencils.
No pencil is marker.

Conclusions:

  1. Some pens are not markers.
  2. No pen is a marker.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
The pen portion inside pencil is not marker.
But other pens may be markers.

Q22.

Statements:
All lions are animals.
Some animals are dangerous.

Conclusions:

  1. Some lions may be dangerous.
  2. All dangerous are lions.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Q23.

Statements:
No A is B.
All B are C.

Conclusions:

  1. No A is C.
  2. All C are A.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

Explanation:
No A is B → B separate.
B → C → so A cannot touch least part of C that contains B.

Q24.

Statements:
All cups are glasses.
Some glasses are steel.

Conclusions:

  1. Some cups are steel.
  2. Some steel are cups.

a) Only 1
b) Only 2
c) Both
d) None

Answer: d) None

Explanation:
Steel may lie outside cups' region.

Q25.

Statements:
Some students are athletes.
All athletes are fit.

Conclusions:

  1. Some students are fit.
  2. All fit are students.

a) Only 1
b) Only 2
c) Both
d) None

Answer: a) Only 1

 

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