Syllogism Notes for Reasoning: Rules, Tricks and Solved Examples

Syllogism is a popular topic of the reasoning section in SSC, banking, railways, defence and state-level examinations. In a syllogism question, you are given two or three statements and a few conclusions, and you have to find which conclusions logically follow from the statements. It is a scoring topic because it has a fixed set of rules, and once you learn them, every question can be solved in under a minute. This note explains the four types of statements, the rules of conclusion, the Venn diagram method, three-statement questions, the either-or case and possibility questions, with many solved examples in simple language.

The Golden Rule

In syllogism, you must accept the statements as true, even if they are absurd in the real world. A statement such as "All cats are dogs" is to be treated as a fact. A conclusion is correct only if it follows definitely from the statements, in every possible situation. Never use outside knowledge. If a conclusion can be false in even one possible situation consistent with the statements, it does not follow.

Four Standard Forms of Statements

Other forms are converted to these four. "Only P are Q" means "All Q are P". "Few P are Q" or "A few" is treated as "Some P are Q" and also suggests "Some P are not Q" in some books, but for the safe approach, use "some". "Every P is Q" and "Any P is Q" mean "All P are Q". "P is not Q" means "No P is Q".

Conversion Rules (What You Can Reverse)

• "All P are Q" can be reversed to "Some Q are P".
• "No P is Q" can be reversed to "No Q is P".
• "Some P are Q" can be reversed to "Some Q are P".
• "Some P are not Q" cannot be reversed.

Combining Two Statements: Result Table

A short way to remember is: All + All gives All; All + No gives No; Some + All gives Some; Some + No gives Some not; No + All gives Some not. If the pair is "All + Some", "Some + Some" or "No + No", there is no definite conclusion.

Solved Examples

Example 1. Statements: All doctors are scientists. No scientist is a farmer. Conclusions: I. No doctor is a farmer. II. Some farmers are doctors. Solution: All + No gives No, so "No doctor is a farmer" follows. Conclusion II contradicts it. So only I follows.

Example 2. Statements: Some roses are flowers. All flowers are plants. Conclusions: I. Some roses are plants. II. All roses are plants. III. Some plants are roses. Solution: Some + All gives Some, so I follows, and its reverse III follows. II is too strong and does not follow. So I and III follow.

Example 3 (three statements). Statements: All cats are dogs. All dogs are rats. Some rats are birds. Conclusions: I. All cats are rats. II. Some rats are cats. III. Some birds are dogs. IV. Some birds are cats. Solution: From the first two statements, All cats are rats (I follows), and its conversion "Some rats are cats" (II follows). For III and IV, the link between birds and dogs or cats is only through "some rats", which does not guarantee overlap with dogs or cats. So only I and II follow.

Either-Or Conclusions

If two conclusions have the same subject and predicate, and form a complementary pair such as (Some P are Q, No P is Q) or (Some P are Q, Some P are not Q), and neither follows individually, then either I or II follows, since one of them must be true. Example: Statements: All lions are tigers. Some tigers are bears. Conclusions: I. Some lions are bears. II. No lion is a bear. Solution: All + Some gives no definite conclusion, so neither I nor II follows alone. But they form a complementary pair, and at least one of them must be true. So either I or II follows. Check that you apply this rule only when neither conclusion follows separately.

Possibility Conclusions

Some questions have conclusions with "may", "can" or "possibly", such as "Some doctors may be farmers". A possibility is true if it does not contradict the statements. If the statements say "No doctor is a farmer", then the possibility is false. But if the statements say "Some scientists are doctors", then "Some doctors may be scientists" is true, since it is already definite. If there is no link in the statements, a possibility between two terms is usually true unless a statement explicitly separates them. Be careful about "Some P are Q" and "No P is Q" in the same question: the first makes "No P is Q" impossible.

Venn Diagram Method in Brief

When rules do not help, draw the diagram. For each statement, draw the circles in all possible ways. For example, for "All P are Q" and "Some Q are R", the circle of R can overlap Q fully with P, or only with part of Q outside P, or may not touch P at all. A conclusion that holds in every such drawing is definite; one that holds only in some drawings is a possibility; one that fails in every drawing is false. Practise drawing quickly and neatly; use dotted lines for uncertain parts.

Common Mistakes

Students often reverse "All P are Q" into "All Q are P"; assume that "Some" means "Some not"; use general knowledge to accept a conclusion; forget to check the either-or case; or confuse "Only" statements. They also treat a possibility as a definite conclusion. Remember that a conclusion must be true in every case, not just in the picture you drew first.

Practice Set With Answers

Solve these before looking at the answers. Question 1: Statements: All pens are books. Some books are tables. Conclusions: I. Some pens are tables. II. Some tables are books. Answer: only II follows, because All + Some gives no definite conclusion, and "Some books are tables" reverses to "Some tables are books". Question 2: Statements: No bus is a car. All cars are vehicles. Conclusions: I. Some vehicles are not buses. II. No bus is a vehicle. Answer: only I follows, since No + All gives Some not. Question 3: Statements: Some dogs are cats. No cat is a mouse. Conclusions: I. Some dogs are not mice. II. All dogs are cats. Answer: only I follows, because Some + No gives Some not. Question 4: Statements: All apples are fruits. All fruits are tasty. Conclusions: I. All apples are tasty. II. Some tasty things are apples. Answer: both follow. If you got all four right, you have understood the rule table well.

Time Management in the Examination

Syllogism questions are usually given in sets of five or more, each with two or three conclusions. Aim to solve each set in about two minutes. Read the statements once, convert them to the standard forms in your mind, use the table, and mark the answer. Draw a diagram only when necessary. If a set looks too confusing, leave it for the end. Since some exams have negative marking, avoid guessing without evidence, but if you can remove two options, a guess is often worthwhile. With one hour of focused practice daily for a week, most students reach a stage of near-perfect accuracy in this topic.

Quick Revision

• All + All = All; All + No = No; Some + All = Some; Some + No = Some not; No + All = Some not.
• Reverse: All to Some; No to No; Some to Some; Some not cannot be reversed.
• Either-or: same subject and predicate, complementary pair, neither follows alone.

Syllogism is a rule-based topic, and consistent practice gives full marks. Learn the table, solve ten questions daily for a week, and you will find yourself solving them in 30 seconds each.

Related Notes to Read Next

Continue your preparation with these related notes from the same subject:

• Blood Relations Notes for Reasoning
• Coding-Decoding Notes for Reasoning
• Direction Sense and Seating Arrangement Notes for Reasoning
• All Reasoning notes

Frequently Asked Questions (FAQ)

What is syllogism in reasoning?

Syllogism is a type of logical reasoning in which you decide which conclusions follow from the given statements, treating the statements as true.

What are the four types of statements in syllogism?

They are All P are Q, No P is Q, Some P are Q and Some P are not Q.

What does "Some" mean in syllogism?

"Some" means at least one and may be all. It does not mean that the rest are different.

Can I reverse "All P are Q"?

Yes, but only as "Some Q are P". It cannot be reversed as "All Q are P".

What is the result of All + No?

All P are Q and No Q is R gives No P is R, which also reverses to No R is P.

What is the result of No + All?

No P is Q and All Q are R gives Some R are not P.

When is either-or applicable?

It applies when two conclusions have the same subject and predicate, form a complementary pair such as Some and No, and neither follows individually.

What if there is no definite conclusion from statements?

Choose the option "none follows" if no conclusion is definitely true. Check for an either-or situation before that.

How do I treat the word "Only" in syllogism?

"Only P are Q" is converted to "All Q are P".

What is a possibility conclusion?

A possibility conclusion uses words such as may or can. It is true if it does not contradict the statements.

How do I solve a three-statement syllogism?

Combine the statements two at a time using the rules, then combine the result with the third statement and check each conclusion.

Should I draw Venn diagrams for every question?

Use the rule table for speed. Draw Venn diagrams when the rules are unclear, or when checking possibilities.