Maharashtra Police Constable – Reasoning Ability
Topic: Statement & Conclusion
The “Statement & Conclusion” skill tests your ability to draw logical inferences from a given statement(s).
You are given a factual statement and a conclusion statement. Your job is to decide whether the conclusion necessarily follows (must be true), might be true (may be true), or cannot be inferred (cannot be concluded) from the statement.
1. Simple Explanation
| Term | What it means | Example |
|---|---|---|
| Statement | A factual claim that is accepted as true. | “All students of the school are wearing uniforms.” |
| Conclusion | A claim that you need to evaluate based on the statement. | “All students of the school are wearing white uniforms.” |
| Must be true | The conclusion cannot be false if the statement is true. | “All students of the school are wearing uniforms.” → “All students are wearing clothes.” (must be true) |
| May be true | The conclusion could be true or false; the statement does not provide enough info. | “All students of the school are wearing uniforms.” → “All students of the school are wearing white uniforms.” (may be true) |
| Cannot be concluded | The conclusion is logically unrelated or contradicts the statement. | “All students of the school are wearing uniforms.” → “All teachers of the school are wearing uniforms.” (cannot be concluded) |
2. Key Points
| # | Key Point | Why it matters |
|---|---|---|
| 1 | Understand the scope – “All” vs “Some” vs “None”. | Determines the strength of inference. |
| 2 | Check for logical consistency – does the conclusion contradict the statement? | If yes → Cannot be concluded. |
| 3 | Look for missing information – if the statement is neutral about a property, conclusion is May be true. | E.g., statement mentions color? If not, cannot deduce color. |
| 4 | Use simple syllogistic reasoning – a two‑premise logic structure. | Helps keep the deduction systematic. |
| 5 | Remember the order of operations – “All A are B” → “Some A are B” is always true; “All A are B” → “All A are C” is only true if B = C. | Avoids common mistakes. |
3. Worked Example
Statement (S):
“All engineers at the plant are required to wear hard hats.”
Conclusion (C1):
“All employees at the plant are required to wear hard hats.”
Conclusion (C2):
“Some engineers at the plant are required to wear hard hats.”
Conclusion (C3):
“All workers at the plant are required to wear hard hats.”
Step‑by‑Step Analysis
| Conclusion | Logic | Result |
|---|---|---|
| C1 | “All engineers” → a subset of “All employees”. Statement only guarantees engineers, not everyone. | May be true – could be that only engineers wear hats. |
| C2 | “All engineers” → trivially implies some engineers wear hats (the same engineers). | Must be true |
| C3 | “All engineers” → does not involve “workers” (could be non‑engineering staff). | Cannot be concluded |
Take‑away
- When the conclusion expands beyond the subject of the statement, it is May be true unless the statement covers all relevant individuals.
- When the conclusion narrows or repeats the subject, it is Must be true.
- If the conclusion refers to a completely different group, it is Cannot be concluded.
4. Practice Questions
Choose the correct option: Must be true (A), May be true (B), or Cannot be concluded (C).
-
Statement – “All students of the school are wearing spectacles.”
Conclusion – “All students of the school are wearing blue spectacles.”
Answer: B -
Statement – “No driver in the city uses a mobile phone while driving.”
Conclusion – “No driver in the city uses a mobile phone while driving.”
Answer: A -
Statement – “Some doctors in the hospital are allergic to latex.”
Conclusion – “No doctor in the hospital is allergic to latex.”
Answer: C -
Statement – “All teachers at the college are senior citizens.”
Conclusion – “All staff at the college are senior citizens.”
Answer: C -
Statement – “All employees of the firm are required to complete the safety drill.”
Conclusion – “All employees of the firm are required to complete the safety drill.”
Answer: A
(Try solving before checking the answers to sharpen your inference skills.)
5. Quick Revision Summary
| Concept | How to Identify | Typical Mistake |
|---|---|---|
| Must be true | Conclusion is a direct consequence (subset or identical). | Thinking “all” → “some” is always false. |
| May be true | Conclusion is not contradicted but not guaranteed (missing attribute). | Over‑generalizing “all” to “some”. |
| Cannot be concluded | Conclusion refers to a different group or contradicts the statement. | Assuming chain of “all A → all B” → “all C” when B ≠ C. |
| Use “All / Some / None” | Translate into set logic: ∀x(A→B), ∃x(A∧B), ¬∃x(A∧B). | Forgetting quantifiers. |
| Check for equality | If statement says “All A are B” and conclusion says “All A are C”, only true if B=C. | Assuming “All A are B” → “All A are C” automatically true. |
Quick Tips for the Exam
- Read the statement first, then the conclusion.
- Mark the subject group (e.g., “engineers”) and the property in question (e.g., “wear hard hats”).
- Check if the conclusion’s subject is the same, a subset, or a different group.