Odisha PSC – Reasoning Ability
Topic: Statement & Conclusion
Statement & Conclusion is a common reasoning sub‑section where a statement (fact or observation) is given, followed by a list of conclusions.
The test taker must decide which conclusions logically follow from the statement (i.e. are true), which are false, or which are indeterminate.
1. Simple Explanation
| Term | Meaning |
|---|---|
| Statement | A fact, observation, or hypothesis set as a premise. |
| Conclusion | A claim that might be true, false, or cannot be deduced from the statement. |
Goal:
- Identify valid conclusions (must be true).
- Identify invalid conclusions (cannot be deduced or are contradicted).
- Identify indeterminate conclusions (cannot be determined from the statement alone).
2. Key Points & Rules
| # | Rule | How to Apply |
|---|---|---|
| 1 | Logical Necessity | A conclusion is valid if it is necessarily true whenever the statement is true. |
| 2 | Logical Possibility | A conclusion is possible if it could be true when the statement is true, but is not guaranteed. |
| 3 | Logical Contradiction | A conclusion is invalid if it contradicts the statement. |
| 4 | Missing Information | If the statement does not provide enough data to determine the truth of a conclusion, it is indeterminate. |
| 5 | Quantifiers | Pay attention to “all”, “some”, “none”, “every”, “no”, and “exactly”. They change the scope of a conclusion. |
| 6 | Binary vs. Multiple Choice | Some papers ask you to select all correct conclusions; others ask for exactly one correct conclusion. Read carefully. |
| 7 | Use of Tables | When many entities are involved (people, objects, events), a table helps keep track of attributes. |
| 8 | Logical Operators | AND, OR, NOT, IF‑THEN, IF AND ONLY IF. |
- IF P THEN Q → Q follows only if P is true.
- P OR Q → At least one of them must be true. | | 9 | Reductio ad Absurdum | Assume a conclusion is true; if it leads to a contradiction with the statement, the conclusion is invalid. | | 10 | Avoid Over‑Generalization | A conclusion that applies to all cases when the statement only mentions some cases is incorrect. |
3. Worked Example
Statement
S: “In a class of 30 students, 18 are girls and 12 are boys. Among the girls, 10 are tall. None of the boys is tall.”
Conclusions
A. All tall students are girls.
B. Some girls are not tall.
C. All boys are short.
D. At least one boy is tall.
E. Exactly 8 girls are short.
Analysis
| Conclusion | Evaluate | Result |
|---|---|---|
| A | If a student is tall, we know only girls can be tall (boys none). | Valid – every tall student must be a girl. |
| B | 18 girls – 10 tall = 8 girls short → some girls not tall. | Valid – there are indeed some not tall. |
| C | Since no boy is tall, all boys are short. | Valid – true by definition. |
| D | Contradicts “None of the boys is tall.” | Invalid – impossible. |
| E | 18 girls – 10 tall = 8 short → exactly 8. | Valid – statement gives exact count. |
Answer
Conclusion D is the only invalid one; the rest are valid.
4. Quick Revision Summary
| Topic | Quick Recap |
|---|---|
| Definition | Statement → premise; Conclusion → claim derived from that premise. |
| Purpose | Determine which conclusions are logically forced (true), contradicted (false), or indeterminate. |
| Key Strategy | • Translate qualitative data into quantitative or symbolic form. • Use tables/diagrams for clarity. • Check each conclusion against every clause of the statement. |
| Common Pitfalls | • Treating “some” as “all”. • Ignoring negations (“none”, “no”). • Assuming a conclusion is true just because it is possible. |
| Practice Tips | • Practice with varied quantifiers. • Time yourself: 1–2 min per problem. • Re‑check each conclusion after finding one to avoid oversight. |
Final Practice Question
Statement: “There are 5 cars in the parking lot: 3 are red and 2 are blue. All red cars have at least 4 wheels, but one of the blue cars is missing a wheel.”
Which of the following conclusions necessarily follow?
- All cars have at least 4 wheels.
- The blue car missing a wheel is not red.
- At least one car has 5 wheels.
- No blue car has more than 4 wheels.
Answer: 2 and 4 are valid; 1 is invalid; 3 is indeterminate.
Good Luck!
Practice routinely, and you’ll master the Statement & Conclusion section in no time.