Syllogism Made Easy: Concepts, Types & Examples

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Syllogism Made Easy: Concepts, Types & Examples

Learn the fundamentals of syllogism, a key concept in logical reasoning. Understand types, structures, examples, and tips for solving syllogism questions effectively.

Syllogism: Concept and Details

Syllogism is a form of deductive reasoning that involves drawing a conclusion from two or more premises that are asserted or assumed to be true.

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Definition

A syllogism is a logical argument where a conclusion is inferred from two premises: a major premise and a minor premise.

Basic Structure:

1. Major Premise: All A are B.
2. Minor Premise: C is A.
3. Conclusion: Therefore, C is B.

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Example

Major Premise: All humans are mortal.
Minor Premise: Socrates is a human.
Conclusion: Therefore, Socrates is mortal.

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Types of Syllogisms

1. Categorical Syllogism
   • Premises deal with categories or classes.
   • Example:
     • All dogs are animals.
     • Some pets are dogs.
     • Therefore, some pets are animals.
2. Hypothetical Syllogism
   • Contains “if…then…” statements.
   • Example:
     • If it rains, the ground will be wet.
     • It is raining.
     • Therefore, the ground is wet.
3. Disjunctive Syllogism
   • Contains “either…or…” statements.
   • Example:
     • Either the light is on or the room is dark.
     • The light is on.
     • Therefore, the room is not dark.

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Important Concepts

Validity

A syllogism is valid if the conclusion logically follows from the premises.

Truth

A syllogism is true if the premises are factually correct.

A syllogism can be valid but not true if the premises are false.

Example:

• All fish can fly.
• A salmon is a fish.
• Therefore, a salmon can fly.
• Valid logic, but false premise.

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Common Syllogism Keywords (used in competitive exams)

• All
• Some
• No
• None
• Only
• Not
• At least
• At most

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Tips for Solving Syllogism Questions (Exams like SSC, Bank, etc.)

1. Use Venn Diagrams: Draw circles to represent sets and visualize overlaps.
2. Memorize Standard Patterns:
   • All A are B = A is inside B.
   • Some A are B = partial overlap.
   • No A is B = no intersection.
3. Check for Negative Conclusions carefully.
4. Don’t assume anything beyond the premises.

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Practice Example

Statements:

1. All poets are writers.
2. Some writers are singers.

Conclusions:

1. Some poets are singers.
2. All singers are writers.

Answer: Neither conclusion follows (can’t be deduced directly).

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“Either-Or” Case in Syllogism (Logical Reasoning)

The “Either-Or” case is a special condition in syllogism questions where more than one conclusion seems possible, but only one can be true at a time — making them mutually exclusive.

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Definition

In syllogism, an “Either-Or” conclusion is considered valid only when:

1. Only one of the two conclusions can be true at a time, not both.
2. Both conclusions are individually possible, but cannot be true together.
3. Together they cover all logical possibilities, meaning if one is false, the other must be true.

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Conditions for Valid “Either-Or”

Condition	Requirement
Mutual Exclusivity	Both conclusions cannot be true at the same time
Possibility	Both conclusions can be true individually
Exhaustive	If one is false, the other must be true

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Example

Statements:

1. All fruits are sweet.
2. Some sweets are not fruits.

Conclusions:

1. All sweets are fruits.
2. Some sweets are not fruits.

Analysis:

• Both cannot be true at once (contradictory).
• One must be true.
• So, it is an Either Conclusion 1 or Conclusion 2 follows case.

Correct answer: Either 1 or 2 follows

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Common Mistakes

• Thinking “either-or” applies when both conclusions are false — it doesn’t.
• Marking “either-or” when both conclusions can be true — invalid.
• Applying “either-or” to complementary statements like “some” and “all” without checking exclusivity.

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Key Phrases Indicating Either-Or in Questions

• “Either conclusion I or II follows”
• “Only one can be true”
• “Mutually exclusive conclusions”

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Pro Tip for Exams

• Use Venn diagrams to test individual truth and mutual exclusivity.
• Confirm that if one conclusion is false, the other is definitely true.

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Statements:

1. Some cups are plates.
2. Some plates are bowls.

Conclusions:

1. All cups are bowls.
2. No cup is a bowl.

Answer Options:

A) Only I follows
B) Only II follows
C) Either I or II follows
D) Both follow
E) Neither follows

✅ Correct Answer: C) Either I or II follows

Explanation:
These are complementary and mutually exclusive. Both can’t be true together, but one must be. So it’s an “either-or” situation.

Statements:

• All cars are vehicles.
• Some vehicles are bikes.

Conclusions:

1. All bikes are cars.
2. Some bikes are not cars.

Options:
A) Only conclusion 1 follows
B) Only conclusion 2 follows
C) Either conclusion 1 or 2 follows
D) Both conclusions follow
E) Neither conclusion follows

Statements:

• No flowers are animals.
• Some animals are birds.

Conclusions:

1. Some birds are flowers.
2. No birds are flowers.

Options:
A) Only conclusion 1 follows
B) Only conclusion 2 follows
C) Either conclusion 1 or 2 follows
D) Both conclusions follow
E) Neither conclusion follows

Statements:

• Some fruits are sweet.
• All sweets are candies.

Conclusions:

1. Some candies are fruits.
2. Some candies are not fruits.

Options:
A) Only conclusion 1 follows
B) Only conclusion 2 follows
C) Either conclusion 1 or 2 follows
D) Both conclusions follow
E) Neither conclusion follows