Statement & Conclusion – RRB JE Reasoning Ability
(A concise study guide for the RRB Junior Engineer exam)
Statement & Conclusion (S&C) questions test your ability to infer what follows from a given statement.
The statement is a factual premise; the conclusion is a logical inference that must be always true, sometimes true, or never true based on that statement.
1. Simple Explanation
| Term | Meaning | Example |
|---|---|---|
| Statement | A given fact or observation that is accepted as true. | All teachers have pens. |
| Conclusion | A logical inference that can be drawn from the statement. | Some teachers have pens. |
- Always: The conclusion is necessarily true whenever the statement is true.
- Sometimes: The conclusion can be true only in some cases when the statement holds.
- Never: The conclusion is impossible if the statement is true.
2. Key Points to Remember
| # | Key Point | Why It Matters |
|---|---|---|
| 1 | Identify the type of statement (categorical, comparative, conditional, etc.) | Different types lead to different inference rules. |
| 2 | Understand the logical form (e.g., “All A are B”, “Some A are B”, “No A are B”) | Determines which conclusions are valid. |
| 3 | Use standard syllogistic patterns (A‑B, B‑C, A‑C) | Many S&C problems are based on syllogisms. |
| 4 | Always consider “some” vs “all” vs “no” | “All” → “Some” is always; “All” → “All” is always; “All” → “No” is never. |
| 5 | Beware of “both” or “neither” | “All A are B” ⇒ “Some A are not B” is impossible. |
| 6 | Check for contradictions | If a conclusion contradicts the statement, it’s “never”. |
| 7 | Use elimination | If only one option satisfies the logical relation, choose it. |
| 8 | Time‑management tip | Quickly write the statement in symbolic form (e.g., ∀x(Ax → Bx)) and test each conclusion. |
3. Worked Example
Statement:
All engineers are proficient in mathematics.
Conclusions (Choose the one that is always true):
A. Some engineers are not proficient in mathematics.
B. All engineers are proficient in mathematics.
C. No engineer is proficient in mathematics.
D. Some engineers are proficient in mathematics.
Step‑by‑Step Solution
| Step | Action | Result |
|---|---|---|
| 1 | Translate the statement: ∀x (Engineer(x) → ProficientMath(x)) | All engineers → they have math skills |
| 2 | Evaluate each conclusion: | |
| A – “Some engineers are not” → contradicts statement (∃x Engineer(x) ∧ ¬ProficientMath(x)) → Never | ||
| B – “All engineers are” → restates statement → Always | ||
| C – “No engineer is” – impossible → Never | ||
| D – “Some engineers are” – logically follows from “All” but not guaranteed (could be all) → Sometimes | ||
| 3 | Choose the answer that is always true → B. |
Answer: B – All engineers are proficient in mathematics.
4. Quick Revision Summary
- Statement = given fact.
- Conclusion = inference that must follow.
- Always – conclusion must hold for every possible scenario consistent with the statement.
- Sometimes – conclusion can hold in some scenarios but not all.
- Never – conclusion contradicts the statement.
- Common patterns
- All A are B → Always: Some A are B; All A are B.
- All A are B → Never: No A are B; Some A are not B.
- Some A are B → Sometimes: Some A are B; Some A are not B.
- No A are B → Always: No A are B.
- Some A are B + No A are C → etc., use syllogistic rules.
- Strategy: Convert to symbolic form, test each conclusion, remember that “all” implies “some” but not vice‑versa.
Use this cheat‑sheet to practice a variety of S&C questions, and you’ll master the logical inference needed for the RRB Junior Engineer exam. Happy studying!