Syllogism – Reasoning Ability
Assam TET – Teacher Eligibility Test
Subject: Reasoning Ability
Topic: Syllogism
Syllogism is a form of deductive reasoning that uses two or more premises to arrive at a logical conclusion. It is a common question type in many competitive exams, including the Assam TET.
1. Simple Explanation
| Element | Definition |
|---|---|
| Premise | A statement that is taken to be true. |
| Conclusion | A statement that logically follows from the premises. |
| Syllogism | A deductive argument with two premises and one conclusion where all three statements are categorical propositions (All/Some/No). |
Typical Structure
- Premise 1 – (type: All/Some/No) + [Subject] + [Predicate]
- Premise 2 – (type: All/Some/No) + [Subject] + [Predicate]
- Conclusion – (type: All/Some/No) + [Subject] + [Predicate]
2. Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Categorical Propositions | Syllogisms use only categorical statements. |
| 2 | Three Terms | Major Term (predicate of conclusion), Minor Term (subject of conclusion), Middle Term (common to both premises). |
| 3 | Distribution of Terms | A term is distributed if it refers to all members of its class. |
| 4 | Validity Rules | - If the middle term is distributed in any premise, it must be distributed in the conclusion. - If a premise contains a negative statement, the conclusion must be negative, and vice‑versa. - The conclusion cannot contain a term that is undistributed in both premises. |
| 5 | Standard Forms | 1. All A are B. 2. Some A are B. 3. No A is B. 4. Some A are not B. |
| 6 | Common Mistakes | - Ignoring the distribution rule. - Mixing up the order of terms. - Assuming a conclusion when a premise is negative. |
| 7 | Answer Options | Usually multiple choice with 4 options; one is the valid conclusion, others are invalid. |
3. Worked Example
Question
All teachers are educators. Some educators are researchers. Which of the following is a valid conclusion?
A. All teachers are researchers.
B. No teachers are researchers.
C. Some teachers are researchers.
D. Some educators are teachers.
Step‑by‑Step Solution
-
Identify the terms
- Major Term (predicate of conclusion): researchers
- Minor Term (subject of conclusion): teachers
- Middle Term (common to premises): educators
-
Rewrite premises
- Premise 1: All teachers are educators. (All A are B)
- Premise 2: Some educators are researchers. (Some B are C)
-
Check the validity rules
- Rule 1 (Distribution of Middle Term)
- Middle term educators is distributed in Premise 1 (All A are B → B is distributed).
- Therefore, the conclusion must distribute educators.
- Rule 2 (Distribution of Minor Term)
- Minor term teachers is not distributed in any premise.
- So the conclusion must not distribute teachers → conclusion must be Some (not All or No).
- Rule 3 (Negative Premise)
- No premise is negative → conclusion must be affirmative.
- Rule 1 (Distribution of Middle Term)
-
Form the only possible conclusion
- Must be Some teachers are researchers (affirmative, minor term undistributed, middle term distributed).
- That matches option C.
Answer: C. Some teachers are researchers.
4. Quick Revision Summary
| Aspect | Quick Points |
|---|---|
| Terminology | Premise, Conclusion, Major, Minor, Middle |
| Categorical Forms | All, Some, No, Some not |
| Distribution Rules | Distributing middle → conclude distributes it; negative premise → negative conclusion |
| Validity Checklist | 1) Middle term distributed in conclusion. 2) No affirmative conclusion with a negative premise. 3) No conclusion with a term undistributed in both premises. |
| Common Patterns | 1. All A are B. 2. Some B are C. → Some A are C. |
| Tips | • Draw a diagram (Venn or simple table). • Read each premise carefully for “all” vs “some”. • Watch for negations (“not”). • Practice with at least 30 problems before exam. |
Quick Practice Problem (for self‑check)
Premise 1: No dancer is a singer.
Premise 2: Some musicians are dancers.
Conclusion?
-
Identify terms:
- Major: singers
- Minor: musicians
- Middle: dancers
-
Check rules:
- Premise 1 is negative → conclusion must be negative.
- Middle term dancers is distributed in Premise 1 → conclusion must distribute dancers → conclusion must be No musicians are singers.
Answer: No musicians are singers.
End of Notes
Use these points as a cheat‑sheet for quick revision before the Assam TET. Good luck!