Study Notes – Statement & Conclusion (Reasoning Ability)
Coast Guard – Reasoning Ability Module
1. Simple Explanation
In a Statement & Conclusion question, you are given one or more statements (facts, premises) and a conclusion.
Your task is to decide whether the conclusion logically follows from the statements.
| Conclusion | Verdict |
|---|---|
| Correct (always true) | The conclusion must be true if the statements are true. |
| Incorrect (always false) | The conclusion cannot be true if the statements are true. |
| Cannot be determined | The conclusion may be true or false; the statements do not provide enough information. |
Think of the statements as a truth set. The conclusion must be a logical consequence of that set.
2. Key Points
| # | Point | Why it matters |
|---|---|---|
| 1 | Terminology | All, some, no; are, is, are not; and, or, if…then. |
| 2 | Logical Consequence | A conclusion is a consequence if it is true in every model that satisfies the statements. |
| 3 | Types of conclusions | - Correct (necessary) - Incorrect (impossible) - Indeterminate (not forced) |
| 4 | Common Pitfalls | - Confusing “some” with “all” - Assuming “If A then B” is equivalent to “A ⇒ B” (but note the converse is not guaranteed) - Neglecting the universal scope of “All” |
| 5 | Step‑by‑Step Approach | 1. List all statements. 2. Translate into logical form (if needed). 3. Check if the conclusion is a logical consequence. 4. Decide verdict. |
| 6 | Time‑Saving Tips | - Look for direct matches (“All X are Y” → “X is Y”). - Check for contradiction (“All X are Y” + “No X are Y”). - Use counter‑example to test “cannot be determined”. |
| 7 | Practice Patterns | 1. Single statement, single conclusion. 2. Two statements, one conclusion. 3. Conditional statements (“If A then B”). 4. Mixed quantifiers (“Some X are not Y”). |
3. Worked Example
Statement
- All amphibians are creatures that can live both in water and on land.
- All frogs are amphibians.
- Not all reptiles are amphibians.
Conclusion
C1. All frogs can live both in water and on land.
Analysis
- From (1): If P is an amphibian → P can live in water and on land.
- From (2): If Q is a frog → Q is an amphibian.
Combine:
- If Q is a frog, then Q is an amphibian (2).
- If Q is an amphibian, then Q can live in water and on land (1).
Thus, Q (frog) can live in water and on land.
Therefore, C1 is a Correct conclusion.
Alternate Conclusion
C2. All reptiles can live both in water and on land.
Check:
- (3) tells us not all reptiles are amphibians.
- We have no information that all reptiles can live in water & on land.
- Counter‑example: Snakes are reptiles that cannot live on land (but can live in water). They are not amphibians.
Hence C2 is Incorrect.
One more Conclusion
C3. Some frogs are not reptiles.
Check:
- We know frogs are amphibians, not reptiles (they are distinct groups).
- There exists at least one frog (any frog) that is not a reptile.
- So C3 is Correct.
4. Quick Revision Summary
| Item | What to Remember |
|---|---|
| Definition | Statement(s) + Conclusion → decide if conclusion follows. |
| Verdicts | Correct, Incorrect, Cannot be determined |
| Common Traps | Misreading “some” vs “all”; assuming converse of implications. |
| Strategy | 1. Translate to simple logic if needed. 2. Check for direct inference or contradiction. 3. If unsure, build a counter‑example. |
| Practice Tip | Work through at least 5 mixed‑quantifier problems a day. |
| Time Hack | If a conclusion is the exact opposite of a given statement, it’s automatically Incorrect. |
| Final Check | Re‑read the conclusion to confirm it is not an inference that goes beyond the statements. |
Remember: In reasoning tests, evidence is king. A conclusion must be forced by the statements; otherwise, mark it as “cannot be determined”.
Good luck with your preparation!