Syllogism – Reasoning Ability (RPF SI)
Syllogism is a form of deductive reasoning that uses a pair of premises to reach a single conclusion.
In RPF SI exams, syllogisms are a staple in the Reasoning Ability section. Mastery of this topic helps you solve a wide range of problems – from logical deduction to pattern‑recognition questions.
1. Simple Explanation
| Term | What it means | Example |
|---|---|---|
| Premise | A statement that is assumed to be true. | All dogs are mammals. |
| Conclusion | A statement that must be true if the premises are true. | All dogs are animals. |
| Syllogism | A logical argument consisting of two premises and a conclusion. | “All A are B. All B are C. → All A are C.” |
In essence, a syllogism is like a logical bridge that connects two truths to reach a third truth.
2. Types of Syllogisms
| Type | Structure | Example |
|---|---|---|
| Universal Positive | All A are B. All B are C. → All A are C. | All roses are flowers. All flowers are plants. → All roses are plants. |
| Universal Negative | No A are B. No B are C. → No A are C. | No cats are dogs. No dogs are fish. → No cats are fish. |
| Particular Positive | Some A are B. Some B are C. → Some A are C. | Some students are seniors. Some seniors are athletes. → Some students are athletes. |
| Particular Negative | Some A are not B. Some B are not C. → Some A are not C. | Some coins are pennies. Some pennies are not 5‑cents. → Some coins are not 5‑cents. |
Tip: In exams, syllogisms are usually universal (i.e., “All” or “No”) and positive (i.e., “All” or “Some”). But keep the other forms in mind for advanced problems.
3. Rules to Solve Syllogisms
- Identify the subject and predicate of each statement.
- Check for overlap: If the first statement talks about A → B, and the second B → C, then the conclusion is A → C. The same applies for negatives.
- Look for common terms: The middle term (B) must be the same in both premises.
- Translate into a Venn diagram (optional but handy).
- Apply the transitive property:
- If A → B and B → C, then A → C.
- If A ↛ B (i.e., No A are B) and B ↛ C, then A ↛ C.
Common Mistake – Mixing up the direction of implication.
All A are B does not mean All B are A.
4. Worked Example
Premise 1: All M’s are Z’s.
Premise 2: All Z’s are P’s.
Conclusion: All M’s are P’s.
Step‑by‑Step
| Step | Action | Reason |
|---|---|---|
| 1 | Identify subjects: M → Z → P | Premises give the chain. |
| 2 | Check transitivity: If every M is a Z, and every Z is a P, then every M must be a P. | Classic All‑All syllogism. |
| 3 | Write conclusion | All M’s are P’s. |
Answer: True.
Another Example (Negative)
Premise 1: No P’s are Q’s.
Premise 2: No Q’s are R’s.
Conclusion: No P’s are R’s.
| Step | Action | Reason |
|---|---|---|
| 1 | Identify middle term: Q | Both premises involve Q. |
| 2 | Apply negative transitivity: If P’s are not Q’s, and Q’s are not R’s, then P’s are not R’s. | Negatives propagate. |
| 3 | Conclude | No P’s are R’s. |
Answer: True.
5. Quick Revision Summary
| Item | Key Point |
|---|---|
| Definition | Two premises → one conclusion. |
| Common Forms | Universal Positive, Universal Negative, Particular Positive, Particular Negative. |
| Middle Term | Must appear in both premises; essential for linking them. |
| Transitive Property | A → B & B → C ⇒ A → C (and same for negatives). |
| Common Pitfalls | Misinterpreting direction, forgetting the middle term, mixing universal with particular forms. |
| Strategy | 1. Write down premises. 2. Identify middle term. 3. Apply transitivity. 4. Verify conclusion. |
Practice Tip:
Create a quick mental chain of the form A → B → C before you write the conclusion. If you can’t form a continuous chain, the syllogism is likely invalid.
Quick Practice Question
Premise 1: Some X’s are Y’s.
Premise 2: All Y’s are Z’s.
Question: Which of the following must be true?
a) Some X’s are Z’s. b) All X’s are Z’s. c) No X’s are Z’s.
Answer: a) Some X’s are Z’s.
Reason: The chain “Some X → Y → Z” guarantees that some X’s belong to Z, not all.
6. Final Takeaway
- Syllogisms are all about logical chaining.
- Always keep the middle term in mind – it’s the bridge between premises.
- Use a Venn diagram or a simple chain diagram for visual clarity.
- Practice with a variety of premise types to build flexibility.
With these notes and a steady practice routine, you