📚 Telangana PSC – Reasoning Ability
Syllogism
Syllogism is a deductive reasoning question that tests your ability to draw a conclusion based on a set of given premises.
The answer is always one of the options provided.
1. Simple Explanation
| Term | Meaning |
|---|---|
| Premise | A statement that is accepted as true (e.g., “All A are B”). |
| Logical Connection | The relationship between premises – e.g., All, Some, None. |
| Conclusion | The statement that follows logically from the premises. |
How it works
- Read the premises carefully.
- Identify the logical relationships (All, Some, None).
- Apply rules of inference (e.g., All A are B + Some B are C → Some A are C).
- Match the conclusion with one of the options.
2. Key Points to Remember
| # | Key Point | Why It Matters |
|---|---|---|
| 1 | All vs. Some vs. None | Determines the scope of the statement. |
| 2 | Logical Hierarchy | “All A are B” → “All A are B” is a universal affirmative. |
| 3 | Transitivity | If A → B and B → C, then A → C (but only for All statements). |
| 4 | Contradiction Check | If a premise contradicts another, the conclusion may be “None”. |
| 5 | Substitution | Replace categories with the given options to see which fits. |
| 6 | Avoid Over‑Interpretation | Stick to what the premises explicitly state. |
| 7 | Speed Strategy | Memorize common inference patterns (All→All, Some→Some, etc.). |
3. Worked Example
Problem
Premises
- All A are B.
- Some B are C.
- No C are D.
Options
a) Some A are D
b) All A are D
c) Some A are C
d) No A are C
Step‑by‑Step Solution
| Step | Action | Reasoning |
|---|---|---|
| 1 | Identify the universal statement: “All A are B.” | Sets the base for inference. |
| 2 | Apply transitivity: “All A are B” + “Some B are C” → “Some A are C.” | Because a subset of B (C) must contain some As. |
| 3 | Check the third premise: “No C are D.” | This is a negative statement – it tells us nothing about As. |
| 4 | Match the derived conclusion “Some A are C” to the options. | Option c is a perfect match. |
Answer: c) Some A are C
4. Quick Revision Summary
| Section | Take‑away |
|---|---|
| Definition | Syllogism = deductive reasoning using premises to find a conclusion. |
| Premises | Always read carefully; look for All, Some, None. |
| Inference Rules | • All A are B + All B are C → All A are C • All A are B + Some B are C → Some A are C • Some A are B + None B are C → No A are C |
| Common Pitfalls | • Assuming “All” implies “None” (false). • Mixing up Some with All. |
| Speed Tip | Memorize the four basic patterns: All‑All, All‑Some, Some‑All, Some‑Some. |
| Practice | Solve at least 10 syllogism questions daily; review mistakes. |
Quick Practice Question
Premises
- Some X are Y.
- No Y are Z.
- All X are W.
Options
a) Some W are Z
b) No W are Z
c) Some W are Y
d) All W are Z
Answer: b) No W are Z (since X ⊆ W and no Y (subset of X) are Z → none of W are Z).
Final Tips
- Read once, think once.
- Write down the three premises in a simple notation (e.g., A→B, B→C).
- Use elimination: cross out options that contradict premises.
- Check for “None”: if any premise states a negative relationship, “None” is often the answer.
Good luck with your preparation!