Syllogism Notes for SSC Exams

Syllogism is a reasoning topic in which two or three statements are given, and you have to decide which conclusions follow from them. It is asked in almost every SSC Reasoning paper, and it becomes easy when you learn the four types of statements, the conversion rules and the conclusion table. These syllogism notes for SSC explain the rules, the Venn diagram method and the either-or case with solved examples and practice questions.

Four Types of Statements

Conversion Rules

Conclusion Table for Two Statements

Use this table when the middle term is common in both statements, such as B in "A and B" and "B and C".

Step-by-Step Method

1. Write the statements one below the other and find the common term.
2. Draw a Venn diagram for each statement, using the standard shapes.
3. Join the diagrams in all possible ways.
4. Accept only the conclusion that is true in every possible diagram.
5. If two conclusions form a complementary pair and neither is definite, check for the "either-or" case.

Venn Diagram Shapes

Either-Or Case

• The case applies when the two conclusions have the same subject and predicate and form a complementary pair.
• Pairs: "Some A are B" and "No A is B"; "All A are B" and "Some A are not B".
• Both conclusions together cover all the cases, so one of them must be true, but neither is definite alone.
• Do not apply the either-or case when one of the conclusions already follows.

Solved Examples

Example 1. Statements: All pens are books. All books are tables.
Conclusions: (I) All pens are tables. (II) Some tables are pens.
From the table, All A are B + All B are C gives All pens are tables, so I follows. Its converse, Some tables are pens, also follows. Answer: both I and II follow.

Example 2. Statements: Some cars are buses. No bus is a truck.
Conclusion: Some cars are not trucks.
Some + No gives "Some are not". Answer: the conclusion follows.

Example 3. Statements: All dogs are cats. Some cats are rats.
Conclusion: Some dogs are rats.
All + Some gives no definite conclusion. Answer: the conclusion does not follow.

Possibility Conclusions

• A conclusion with "can be" or "may be" is true if it is possible in at least one diagram.
• If a definite relation is given by the statements, the opposite "possibility" cannot be true.
• Example: for "All A are B", the conclusion "Some A can be B" is true.

Quick Tips

• Memorise the conclusion table, because it solves most questions in a few seconds.
• Never take a general idea from real life; accept only what the statements say.
• Check the converse of the statement, because it often gives the second conclusion.
• Use the Venn diagram when the table gives no answer.

Quick Revision Points

• All + All gives All, and All + No gives No.
• Some + All gives Some.
• No + All gives Some not.
• Some A are not B cannot be converted.
• The either-or case needs a complementary pair with the same subject and predicate.

Practice Questions With Answers

1. Statements: All A are B. All B are C. Does "All A are C" follow?
   Answer: Yes
2. Statements: All A are B. Some B are C. Does "Some A are C" follow?
   Answer: No
3. Statements: No A is B. All B are C. Does "Some C are not A" follow?
   Answer: Yes
4. Statements: Some A are B. No B is C. Does "Some A are not C" follow?
   Answer: Yes
5. What is the converse of "Some A are B"?
   Answer: Some B are A
6. What is the converse of "No A is B"?
   Answer: No B is A
7. Can "Some A are not B" be converted?
   Answer: No
8. Statements: Some A are B. Some B are C. Does "Some A are C" follow?
   Answer: No
9. Which pair forms an either-or case?
   Answer: Some A are B and No A is B
10. Statements: All A are B. All C are B. Does "All A are C" follow?
    Answer: No

How to Practise This Chapter

Practise ten syllogism questions daily and write the conclusion table from memory every morning. Then attempt timed sets from our practice papers and the previous year papers page. Read the next chapter, Clock and Calendar, and see all topics on the Reasoning notes page. Syllogism is closely linked with Logical Venn Diagram.

Frequently Asked Questions

What is syllogism?

Syllogism is a reasoning topic in which conclusions are drawn from two or more given statements using logic.

What are the four types of statements in syllogism?

They are All A are B, No A is B, Some A are B and Some A are not B.

How do I solve syllogism quickly?

Learn the conclusion table and conversion rules, and use the Venn diagram when the answer is not clear.

What is conversion in syllogism?

Conversion means reversing the subject and the predicate of a statement, such as changing "Some A are B" to "Some B are A".

Which statements can be converted?

"No A is B" and "Some A are B" convert to the same form, and "All A are B" converts to "Some B are A". "Some A are not B" cannot be converted.

What is the either-or case?

It is the case where two conclusions are complementary and one of them must be true, but neither is definite alone.

What does All + Some give in syllogism?

All A are B and Some B are C do not give any definite conclusion.

What is a possibility conclusion?

A conclusion with "can be" is true if it is possible in at least one Venn diagram.

Should I use my general knowledge in syllogism?

No. Accept the statements as true even if they look false in real life, and use only the given statements.

How many questions come from syllogism in SSC exams?

Usually two to five questions come from syllogism in SSC Reasoning papers, but the number changes from year to year.

Is the Venn diagram method better than the table?

The table is faster, and the Venn diagram is more reliable for difficult cases, so learn both.

How much time should I spend on one syllogism question?

Spend about 30 to 40 seconds with the conclusion table.