Study Notes – Reasoning Ability
Topic: Statement & Conclusion
1. Simple Explanation
In a Statement & Conclusion problem you are given a set of statements (premises) and one or more conclusions.
Your task is to decide whether the conclusion necessarily follows from the statements, i.e. whether it is logically true in all cases consistent with the statements.
- Conclusion → a claim that might be true or false.
- Statement → facts that are given and are accepted as true.
The goal is to test logical inference: From what is given, can we deduce the conclusion?
2. Key Points (What to Remember)
| # | Point | Why It Matters |
|---|---|---|
| 1 | Identify all premises | The conclusion must be derived only from the given statements. |
| 2 | Look for explicit “if…then” patterns | These give direct conditional relationships. |
| 3 | Use transitive reasoning | If A → B and B → C, then A → C. |
| 4 | Check for “only if / if and only if” | “Only if” sets an upper bound; “if and only if” gives equivalence. |
| 5 | Beware of negative statements | “Not” flips the truth value; ensure you interpret them correctly. |
| 6 | Avoid assuming extra facts | Conclusions must be supported solely by the given statements. |
| 7 | Determine the type of answer | |
| • Yes – conclusion follows necessarily. | ||
| • No – conclusion does not follow. | ||
| • Cannot be determined – conclusion could be true or false. | ||
| 8 | Use diagrammatic or truth‑table methods for complex chains. | Helps visualise logical flow. |
3. Step‑by‑Step Method
- List all statements in a clear, numbered fashion.
- Translate each statement into a logical form (e.g., “If A, then B” → A → B).
- Combine statements using logical inference rules (Modus Ponens, Modus Tollens, Hypothetical Syllogism, etc.).
- Reach the conclusion: see if it appears in the inferred set.
- Decide:
- If the conclusion appears → Yes.
- If the conclusion is contradicted or not implied → No.
- If the conclusion could be either true or false → Cannot be determined.
4. Worked Example
Statements
- If a person studies hard, then he gets good grades.
- If a person gets good grades, then he is considered successful.
- Rahul studies hard.
Conclusion
- Rahul is considered successful.
| Step | Action | Reasoning |
|---|---|---|
| 1 | Translate | 1 → Studying → Good Grades 2 → Good Grades → Successful 3 → Studying (given) |
| 2 | Apply Modus Ponens | From 3 and 1 → Rahul gets good grades. |
| 3 | Apply Modus Ponens again | From Rahul gets good grades and 2 → Rahul is considered successful. |
| 4 | Check conclusion | It matches the derived statement. |
Answer: Yes – The conclusion follows necessarily.
A “No” Example
Statements
- If a person studies hard, then he gets good grades.
- If a person gets good grades, then he is considered successful.
- Rahul has not studied hard.
Conclusion
- Rahul is considered successful.
Analysis
- From 3 we cannot infer Rahul gets good grades.
- Without good grades, we cannot apply statement 2.
- Therefore, the conclusion cannot be guaranteed.
Answer: No – The conclusion does not follow.
A “Cannot be determined” Example
Statements
- If it rains, the match is cancelled.
- The match is cancelled.
Conclusion
- It is raining.
Analysis
- From statement 1 we know: Rain → Cancel.
- Statement 2 gives Cancel, but this does not imply Rain (other reasons could cancel).
- So the conclusion might be true or false.
Answer: Cannot be determined.
5. Quick Revision Summary
| Item | What to Do | Quick Tip |
|---|---|---|
| Read all statements | Note each premise. | Don’t skip any. |
| Convert to logic | Use “if…then” → → | Keep it simple. |
| Chain them | Apply inference rules. | Modus Ponens = A → B, A gives B. |
| Check conclusion | Is it in the derived set? | If yes → Yes; if contradicted → No. |
| Check for ambiguity | Could be true or false? | If insufficient info → Cannot be determined. |
| Avoid extra assumptions | Stick to given facts. | No “extra” facts → no “sneaky” conclusions. |
Practice Tip:
Before solving, write a small truth table for the key variables. It often reveals whether the conclusion is forced, impossible, or optional.
Happy practicing!