Telangana PSC – Reasoning Ability
Topic: Statement & Conclusion
In a “Statement & Conclusion” question you are given two or more statements (facts/observations) and one conclusion.
You must decide whether the conclusion necessarily follows from all the statements, cannot follow, or may follow (i.e., could be true).
1. Simple Explanation
| Term | What it means | Example |
|---|---|---|
| Statement | A factual, non‑contradictory piece of information supplied in the question. | “All students are present.” |
| Conclusion | A claim you have to test against the statements. | “No student is absent.” |
| Conclusion type | Three possible answers: | |
| (A) Follows – It is logically certain that the conclusion is true if all statements are true. | If every student is present, then obviously no student is absent. | |
| (B) Cannot follow – It is logically impossible that the conclusion is true if all statements are true. | If all students are present, then “Some students are absent” cannot be true. | |
| (C) May follow – The conclusion can be true or false; the statements do not guarantee its truth. | If all students are present, “Some students are late” could be true or false. |
2. Key Points to Remember
| # | Point | Why it matters |
|---|---|---|
| 1 | Read carefully | Mis‑reading a statement can change the conclusion’s status. |
| 2 | Check for logical necessity | A conclusion must be true in every possible scenario that satisfies all statements. |
| 3 | Avoid assuming additional facts | Only use the information given. |
| 4 | Use contraposition | If a statement is “If A then B”, the converse “If not B then not A” is not automatically true. |
| 5 | Look for exclusive vs inclusive conditions | “All X are Y” vs “Some X are Y”. |
| 6 | Consider counter‑examples | To prove “cannot follow”, find a single scenario where statements are true but conclusion false. |
| 7 | Simplify the statements | Convert into simple logical forms: A → B, A ∧ B, ¬A, etc. |
| 8 | Practice pattern recognition | Common patterns: (i) “All A are B” + “All B are C” → “All A are C” (Follows). |
| 9 | Keep time | Usually 10–15 minutes; skip hard ones if time’s tight and return if possible. |
| 10 | Eliminate options | In multiple‑choice, eliminate “cannot follow” first; then check “follows” and “may follow”. |
3. How to Solve a Statement & Conclusion Question
- Identify the statements – Write them down separately.
- Translate into logical notation (optional but helpful).
- Check for direct inference – Does the conclusion directly follow from one statement?
- Check for indirect inference – Combine statements to derive a new fact.
- Search for a counter‑example – If you find any, the conclusion cannot follow.
- If no counter‑example, then the conclusion may follow.
- If you prove it must always be true, mark it as follows.
4. Worked Example
Statements
- All paintings are artworks.
- Some artworks are not sculptures.
- No sculptures are paintings.
Conclusion
- The conclusion: All paintings are not sculptures.
Step‑by‑step
| Step | Reasoning |
|---|---|
| 1 | Analyze Statement 1: Painting → Artwork. |
| 2 | Analyze Statement 3: Painting → ¬Sculpture. (No sculptures are paintings). |
| 3 | Conclusion: “All paintings are not sculptures” is equivalent to Painting → ¬Sculpture. |
| 4 | This is exactly the same as Statement 3. |
| 5 | Since Statement 3 guarantees the conclusion, the conclusion follows from the statements. |
Answer: A – Follows
Counter‑example method (if needed)
Suppose you suspect the conclusion might not follow.
Try to construct a scenario where all statements are true but the conclusion is false.
If you succeed, the correct answer is B – Cannot follow.
If you cannot find any such scenario, the conclusion may follow.
5. Quick Revision Summary
| Item | What to keep in mind |
|---|---|
| Definition | Statements = facts; Conclusion = claim to test. |
| Answer options | Follows, Cannot follow, May follow. |
| Key logic | – Direct inference ✔️ – Counter‑example ❌ |
| Common patterns | 1. All A are B + All B are C → All A are C (Follows) 2. All A are B + Some B are not C → Some A are not C (May follow) 3. Some A are B + All B are C → Some A are C (Follows) |
| Tips | • Translate to logic • Look for exclusivity • Eliminate “cannot follow” first • Time‑management |
| Practice | Solve 10–15 sample questions daily; review mistakes. |
Final Note:
Mastering Statement & Conclusion questions comes down to logical rigor and pattern recognition. Keep practicing, and you’ll be able to swiftly identify whether a conclusion is certain,