Syllogism – Reasoning Ability (Nagaland Police Sub‑Inspector)
A syllogism is a deductive argument that contains three parts:
- Two premises (major & minor)
- A conclusion that follows logically from the premises.
The task in exams is to decide whether the conclusion is valid (must be true if premises are true) or invalid (may be false even if premises are true).
Commonly, syllogisms are categorical (dealing with categories of things) and written in the format:
All A are B.
All B are C.
∴ All A are C.
1. Simple Explanation
| Term | Definition |
|---|---|
| Major Premise | General statement that provides the main rule (e.g., “All A are B”). |
| Minor Premise | Specific statement that applies the rule to a particular case (e.g., “All B are C”). |
| Conclusion | Statement that follows from the two premises (e.g., “All A are C”). |
| Validity | The conclusion must be true whenever the premises are true. |
| Soundness | A valid syllogism whose premises are actually true. |
Why it matters: Police exams often ask you to spot the logical connection, not just factual knowledge.
2. Key Points to Remember
| Feature | What to Check | Typical Mistakes |
|---|---|---|
| Form of the syllogism | Identify the structure (A‑B‑C, A‑B¬C, etc.). | Confusing “All A are B” with “No A are B”. |
| Predicate & Subject | Determine which word is the predicate (property) and which is the subject (class). | Mixing up subject and predicate. |
| Validity rules | Use the 19 standard categorical syllogism forms (e.g., Barbara, Celarent, Darii). | Assuming any “All‑All” works; ignoring the middle term. |
| Middle Term | The term that appears in both premises but not in the conclusion. It must be distributed in at least one premise. | Forgetting the middle term can lead to invalid conclusions. |
| Distribution | A term is distributed when it refers to all members of its class (e.g., “All A are B” distributes A but not B). | Misreading distribution; e.g., “Some A are B” distributes A but not B. |
| Fallacies | 1. Illicit major/minor (non‑distributed middle term). 2. Illicit conversion (swapping terms in a premise). 3. Extended syllogism (more than three terms). | Over‑extending the premises. |
3. Worked Example
Problem
Major Premise: All S (students) are P (passable).
Minor Premise: No P (passable) are G (good).
Conclusion: Therefore, no S (students) are G (good).
Step‑by‑Step Analysis
| Step | Action | Result |
|---|---|---|
| 1 | Identify terms | S = students, P = passable, G = good |
| 2 | Check distribution | - Major: S distributed, P not. - Minor: P distributed, G not. Middle term P is distributed in the minor premise → OK. |
| 3 | Apply validity rule | The form is “All S are P; No P are G; ∴ No S are G.” This is the syllogism Darii (A‑E‑I). Valid. |
| 4 | Conclusion | “No students are good.” The conclusion must be true if the premises are true. |
Common Trap
If the minor premise were “Some P are G” instead of “No P are G”, the middle term would be undistributed, making the syllogism invalid.
4. Quick Revision Summary
| Category | What to Remember |
|---|---|
| Premises | 1. Major (general), 2. Minor (specific) |
| Conclusion | Must logically follow from both premises |
| Middle Term | Appears in both premises, must be distributed at least once |
| Distribution | “All A are B” → A distributed, B not; “No A are B” → both distributed |
| Valid Forms | 19 standard categorical syllogisms (Barbara, Celarent, Darii, etc.) |
| Common Fallacies | Illicit major/minor, illicit conversion, extended syllogism |
| Checking Validity | 1. Identify terms and distribution. 2. Match form to a valid syllogism. 3. Verify conclusion. |
Quick Practice Question
Major: No A are B.
Minor: All C are A.
Conclusion: All C are not B.
| Is the conclusion valid? | Why? |
|---|---|
| ✅ | The form is E‑A‑I (Celarent): “No A are B; All C are A; ∴ No C are B.” The conclusion is “No C are B” (the same as “All C are not B”). |
Use this template to check any syllogism quickly before choosing the answer. Good luck with your preparation!