Syllogism
Reasoning Ability – Arunachal Pradesh Police Constable (APPC) Examination
1. Simple Explanation
A syllogism is a deductive argument consisting of two premises (statements) that lead to a single conclusion.
It is a logical tool used to test reasoning, inference, and the ability to spot contradictions.
General Form
Premise 1: All A are B
Premise 2: C is A
Conclusion : C is B
The premises must be true and logically connected; otherwise, the conclusion will be false.
2. Key Points
| # | What to Look For | Why It Matters |
|---|---|---|
| 1 | Validity | A syllogism is valid if the conclusion necessarily follows from the premises. |
| 2 | Soundness | Even a valid syllogism is unsound if one premise is false. |
| 3 | Logical Connectives | “All”, “Some”, “No”, “Not” – each changes the inference pattern. |
| 4 | Type of Syllogism | Universal (All), Particular (Some), Negative (No, Not). |
| 5 | Figure | Position of the middle term (the shared term) determines the figure (1‑4). |
| 6 | Common Errors | • “All A are B” & “Some B are C” does not imply “Some A are C”. • “No A are B” & “All C are A” does not imply “No C are B”. |
| 7 | Logical Rules | • Obligatory Middle Term – must appear in both premises. • No Contradiction – premises cannot be mutually exclusive. • Inclusion – if a term is universal, the conclusion must also be universal or particular accordingly. |
| 8 | Common Patterns | • All A are B. All B are C. Therefore, All A are C. • All A are B. Some C are A. Therefore, Some C are B. • Some A are B. All B are C. Therefore, Some A are C. |
| 9 | Practice Tip | Convert each statement into a categorical form (All, Some, No, Not) before proceeding. |
3. Worked Example
Given
- Premise 1 – All students are diligent.
- Premise 2 – Some teachers are students.
Question – Which of the following conclusions is logically valid?
A. Some teachers are diligent.
B. All teachers are diligent.
C. No teachers are diligent.
D. Some teachers are not diligent.
Step‑by‑Step Solution
| Step | Action | Explanation |
|---|---|---|
| 1 | Identify terms | A = teachers, B = students, C = diligent. |
| 2 | Write premises in categorical form | 1) All B are C. 2) Some A are B. |
| 3 | Locate the middle term | B (students) appears in both premises. |
| 4 | Determine figure | Middle term is in the middle of both premises → Figure 2. |
| 5 | Recall rule for Figure 2 (All‑Some) | If “All B are C” & “Some A are B” → Some A are C is valid. |
| 6 | Match with options | Option A: Some teachers are diligent. ✅ |
| 7 | Verify others | B: All teachers are diligent – requires “All A are B” (false). C: No teachers are diligent – contradicts premise 1. D: Some teachers are not diligent – no support. |
Answer: A. Some teachers are diligent.
4. Quick Revision Summary
- Syllogism = 2 premises → 1 conclusion.
- Key Terms: All, Some, No, Not.
- Middle Term must appear in both premises.
- Figure (1‑4) depends on the position of the middle term.
- Validity: Conclusion must follow logically.
- Soundness: All premises must be true.
- Common Mistake: Assuming “All A are B” + “Some B are C” → “Some A are C”.
- Practice: Convert statements to categorical form; then match with known syllogistic patterns.
Quick Checklist for Every Question
- Re‑write each statement as All/Some/No/Not X are Y.
- Identify the middle term (shared between premises).
- Determine the figure.
- Apply the standard rule for that figure.
- Select the conclusion that matches the rule.
Use this flow, and you’ll crack most syllogism questions in the APPC Reasoning Ability section!