Syllogism

Syllogism is a topic where two or more statements are given and you have to check which conclusions logically follow from those statements. The statements may or may not be true in real life - you have to assume them as true and only check the logic.

This is one of the most important topics in SSC CGL Reasoning - 3 to 4 questions come every year.

Golden Rule:

Always assume the given statements are 100% true even if they seem wrong in real life.

Example: 

Statement: All cats are dogs. Even though this is wrong in real life - for syllogism you MUST assume it is true.

Basic Concepts:

Universal Positive (All A are B)

• All cats are animals.
• Means: Every single cat is an animal. No exception.

Universal Negative (No A is B)

• No cat is a dog.
• Means: Not even a single cat is a dog.
•  

Particular Positive (Some A are B)

• Some cats are animals.
• Means: At least one cat is an animal.

Particular Negative (Some A are not B)

• Some cats are not dogs.
• Means: At least one cat is not a dog.

The Venn Diagram Method - Easiest Way:

Draw circles to represent each group and check if the conclusion is always true.

Example 1: 

Statement 1: All dogs are animals. 

Statement 2: All animals are living beings. 

Conclusion: All dogs are living beings.

Draw it: 

Dogs circle is inside Animals circle. 

Animals circle is inside Living Beings circle. 

So Dogs circle is also inside Living Beings circle. 

Conclusion FOLLOWS. ✅

Example 2: 

Statement 1: All cats are black. 

Statement 2: Some black things are tables. 

Conclusion: Some cats are tables.

Draw it: 

Cats circle is inside Black circle. 

Tables circle partially overlaps Black circle. 

Tables circle may or may not touch Cats circle. 

Conclusion does NOT follow. ❌

Important Rules to Remember:

Rule 1 - All + All = All 

All A are B. All B are C. Then All A are C. ✅

Rule 2 - All + No = No 

All A are B. No B is C. Then No A is C. ✅

Rule 3 - Some + All = Some 

Some A are B. All B are C. Then Some A are C. ✅

Rule 4 - Some + No = Some Not 

Some A are B. No B is C. Then Some A are not C. ✅

Rule 5 - All + Some = No conclusion 

All A are B. Some B are C. Then we CANNOT say anything about A and C. ❌

Rule 6 - Some + Some = No conclusion 

Some A are B. Some B are C. Then we CANNOT say anything about A and C. ❌

Either-Or Cases:

Sometimes neither conclusion 1 nor conclusion 2 directly follows but together they cover all possibilities. This is called Either-Or case.

Example: 

Statement: Some cats are dogs. Some cats are not dogs. 

Conclusion 1: All cats are dogs. 

Conclusion 2: No cats are dogs. 

Answer: Either conclusion 1 or conclusion 2 follows.

How to Solve Syllogism Questions:

Step 1 - Read all statements carefully. 

Step 2 - Draw Venn diagrams for the statements. 

Step 3 - Check each conclusion against the diagram. 

Step 4 - A conclusion follows only if it is TRUE in ALL possible diagrams. 

Step 5 - If a conclusion is true in some diagrams but not all - it does NOT follow.

Common Mistakes to Avoid:

Mistake 1 - Using real life knowledge instead of logic. 

"All men are mortal" - do not think about real life, only follow the logic.

Mistake 2 - Assuming conclusions that are not directly supported. 

If Some A are B - you cannot conclude All A are B.

Mistake 3 - Forgetting the Either-Or case. 

Always check if two conclusions together cover all possibilities.

Important Tips:

• Always draw Venn diagrams - never solve in your head
• Remember the 6 rules given above
• Practice at least 10 syllogism questions daily
• In SSC CGL, syllogism questions are straightforward - no tricks
• If confused between two conclusions - check if Either-Or case applies