Syllogism – Nagaland TET (Reasoning Ability) Study Notes
Syllogism is a deductive reasoning tool that uses two premises to reach a logical conclusion.
It’s a staple of the TET‐Reasoning section, so mastering its structure and common patterns will give you a big advantage.
1. Simple Explanation
- Premise 1 (Major Premise) – A universal statement (e.g., All A are B).
- Premise 2 (Minor Premise) – A particular statement that relates the subject of the major premise to another element (e.g., C is A).
- Conclusion – A statement that logically follows from both premises (e.g., C is B).
The classic form is A → B and C → A then C → B.
Syllogisms test whether you can spot this logical chain quickly.
2. Key Points
| Category | Details |
|---|---|
| Types of Syllogisms | 1. All‑All (All A are B; All B are C → All A are C) 2. All‑Some (All A are B; Some C are A → Some C are B) 3. Some‑All (Some A are B; All B are C → Some A are C) 4. Some‑Some (Some A are B; Some B are C → Some A are C) |
| Logical Operators | All = universal quantifier (∀). Some = existential quantifier ( ∃). |
| Common Mistakes | - Mixing up All and Some. - Assuming the conclusion is All when it should be Some (or vice‑versa). - Ignoring “No” or “Not” statements. |
| Test Pattern | Usually 4 statements (1 major, 1 minor, 1 conclusion + 1 distractor). Answer options: A, B, C, D, or “None of the above.” |
| Speed Tips | 1. Identify the subject of the conclusion first. 2. Find which premise contains that subject. 3. Trace to the other premise. 4. Check the quantifiers (All/Some). |
3. Worked Example
Statement Set
- All doctors are teachers.
- Some teachers are engineers.
- All engineers are artists.
- Some doctors are artists.
Question: Is statement 4 the correct conclusion from statements 1–3?
Step‑by‑Step Reasoning
| Step | Analysis | Result |
|---|---|---|
| 1 | Identify the conclusion’s subject: Some doctors. | |
| 2 | Find premise containing “doctors”: Premise 1 (All doctors are teachers). | |
| 3 | From Premise 1, doctors → teachers. | |
| 4 | Find premise containing “teachers”: Premise 2 (Some teachers are engineers). | |
| 5 | From Premise 2, some teachers → engineers. Since we only know some teachers are engineers, we cannot say all teachers are engineers. But we only need a link from doctors to engineers. Because all doctors → teachers and some teachers → engineers, we can conclude some doctors are engineers. | |
| 6 | Find premise containing “engineers”: Premise 3 (All engineers are artists). | |
| 7 | From Premise 3, engineers → artists. Combining with step 5: some doctors → engineers → artists. Therefore some doctors are artists. | ✔️ |
| 8 | Conclusion matches statement 4. | ✅ |
Answer: Yes, statement 4 is the correct conclusion.
4. Quick Revision Summary
| Concept | Remember |
|---|---|
| Structure | Major Premise → Minor Premise → Conclusion |
| Quantifiers | All → universal; Some → existential |
| Logical Flow | Subject → Link → Second Premise → Conclusion |
| Common Patterns | 1. All‑All → All 2. All‑Some → Some 3. Some‑All → Some 4. Some‑Some → Some |
| Speed Strategy | 1. Spot conclusion subject. 2. Trace backward through premises. 3. Verify quantifiers match. |
| Practice Tip | Convert each premise into a simple “If‑Then” statement. |
| Final Check | Does the conclusion logically follow with the same quantifier? |
Final Thought
Syllogisms are all about following the logical chain. Treat the first statement as a bridge and the second as a road, then drive straight to the conclusion. With practice, spotting the right path becomes second nature—exactly what you need to ace the TET Reasoning section. Good luck!