Study Notes – Statement & Conclusion
Program: State Agriculture Officer
Subject: Reasoning Ability
Topic: Statement & Conclusion
1. Simple Explanation
In a Statement & Conclusion (S&C) problem you are given a set of statements (facts, observations, or premises) and a conclusion (a claim).
Your task is to decide whether the conclusion logically follows from the statements, contradicts them, or can’t be determined from the given information.
| Term | Meaning |
|---|---|
| Statement | A factual or logical premise that is accepted as true. |
| Conclusion | A claim that may be true, false, or indeterminate based on the statements. |
2. Key Points
| # | Point | Why It Matters |
|---|---|---|
| 1 | Identify the type of inference – Logical (deduction), Probabilistic, or Statistical. | Determines the strength of the conclusion. |
| 2 | Look for explicit contradictions – a conclusion that directly opposes a statement is false. | Quick elimination of false conclusions. |
| 3 | Check for logical necessity – if the conclusion must be true given the statements. | Distinguishes true from cannot be determined. |
| 4 | Beware of hidden assumptions – conclusions may rely on unstated knowledge. | Prevents misclassification as “cannot be determined”. |
| 5 | Use the “All‑A are B” structure – common pattern for logical conclusions. | Helps identify necessary truths. |
| 6 | Count or quantity constraints – statements involving numbers often dictate the conclusion. | Useful for “cannot be determined” scenarios. |
| 7 | Check for “at least one” or “exactly one” clauses – important in problems with multiple subjects. | Avoids wrong inference of uniqueness. |
3. Types of Statements & Conclusions
| Category | Example | Typical Conclusion |
|---|---|---|
| Logical Deduction | All oranges are fruits. | All fruits are oranges. (False – converse) |
| Contrapositive | If X then Y. | If not Y then not X. |
| Statistical Generalization | 80% of farmers use pesticide A. | Therefore, most farmers use pesticide A. |
| Probabilistic (At least/at most) | At least 3 of 5 farmers use irrigation. | Exactly 3 farmers use irrigation. (False) |
4. How to Approach an S&C Question
-
Read Carefully
- Highlight every statement.
- Note any “if‑then”, “all”, “none”, “at least”, “at most” phrases.
-
Translate to Logical Form
- Convert statements into propositional logic or set notation if helpful.
-
Analyze the Conclusion
- Does it directly follow?
- Is it the converse or inverse of a statement?
- Does it require additional assumptions?
-
Check for Contradiction
- If the conclusion contradicts any statement, mark False.
-
Determine Necessity
- If the conclusion is must‑be true given all statements, mark True.
-
If Neither
- If the conclusion is not logically forced and does not contradict, mark Cannot be determined.
5. Worked Example
Statements
- S1: All mango trees produce fruit.
- S2: Some mango trees are located in the orchard.
- S3: No fruit is grown outside the orchard.
Conclusion
C: All fruit in the orchard comes from mango trees.
Analysis
| Step | Observation | Decision |
|---|---|---|
| 1 | From S1: mango trees → fruit. | True |
| 2 | From S2: mango trees ⊆ orchard. | True |
| 3 | From S3: fruit ⊆ orchard. | True |
| 4 | Is every fruit in the orchard from a mango tree? | No. |
| 5 | Counter‑example: a banana tree in the orchard (not mentioned) could produce fruit. | Contradicts conclusion. |
Result: False (Conclusion contradicts the possibility of other fruit sources.)
6. Quick Revision Summary
| Step | Action | Key Take‑away |
|---|---|---|
| 1 | Read all statements | Capture every clause. |
| 2 | Identify logical structure | Recognize “All A are B”, “If A then B”, “At least/at most”. |
| 3 | Translate to logic | Helps see hidden assumptions. |
| 4 | Check for contradictions | If conclusion conflicts with any statement → False. |
| 5 | Check for necessity | If conclusion must hold given all statements → True. |
| 6 | Else | Mark Cannot be determined. |
Quick Practice
Statements
- Some traders are farmers.
- All farmers grow crops.
- No trader buys crops.
Conclusion
All traders grow crops.
Answer: Cannot be determined – because “some traders are farmers” does not guarantee that all traders are farmers.
Tips for Exam
- Redundancy: Ignore statements that do not influence the conclusion.
- “All” vs. “Some”: “All A are B” does not imply “All B are A”.
- Quantifiers: Pay attention to “at least” vs. “exactly”.
- Time‑saving: If you spot a direct contradiction early, skip the rest of the analysis.
Good luck! Master the systematic approach above, and you’ll confidently tackle any Statement & Conclusion problem.