Statement & Conclusion – Reasoning Ability
(Agniveer – Program: Agniveer, Subject: Reasoning Ability)
1. Simple Explanation
| Statement | Conclusion |
|---|---|
| A fact or proposition that is given in the problem. | A claim that logically follows (must be true) from the statement(s). |
In a Statement & Conclusion (S&C) question you are given one or more statements (S) and a list of possible conclusions (C).
You must decide which conclusions are valid given the statements.
Rule of thumb:
- True → True (if a statement is true, any conclusion that is a logical consequence of it is also true).
- False → False (if a statement is false, any conclusion that requires the statement to be true is false).
- If the statement’s truth‑value is unknown or ambiguous, you cannot be sure about the conclusion.
2. Key Points
| # | Concept | What to remember |
|---|---|---|
| 1 | Logic direction | Statements are premises; conclusions are implications. |
| 2 | True, False, Unknown | Identify the truth value of each statement first. |
| 3 | Types of Statements | • Universal statements (All/No) • Particular statements (Some) • Existential statements (There exists) |
| 4 | Logical Connectives | AND, OR, NOT, IMPLIES (if‑then). |
| 5 | Inference Rules | • Modus Ponens (If A → B and A, then B). • Modus Tollens (If A → B and not B, then not A). • Hypothetical Syllogism (If A → B and B → C, then A → C). |
| 6 | Common Pitfalls | • Assuming “All A are B” → “Some A are B” (which is true, but not always). • Ignoring negations. |
| 7 | Answering Strategy | 1. Read all statements carefully. 2. Determine the truth value of each statement. 3. Test each conclusion against the statements. 4. Select only the conclusions that are necessarily true. |
| 8 | Multiple Correct Answers | Some S&C questions allow more than one correct conclusion. |
3. Worked Example
Problem
Statements
- All cars are vehicles.
- Some vehicles are electric.
- No electric cars are gasoline cars.
Conclusions
A. Some cars are electric.
B. Some vehicles are gasoline cars.
C. No cars are gasoline cars.
D. All vehicles are cars.
Step‑by‑Step Solution
| Step | Action | Result |
|---|---|---|
| 1 | Identify truth values | All given statements are true (they are the premises). |
| 2 | Analyze Conclusion A | “Some cars are electric.” From (1) & (2): We know some vehicles are electric, but we don’t know if those electric vehicles are cars. Thus, Conclusion A cannot be guaranteed. |
| 3 | Analyze Conclusion B | “Some vehicles are gasoline cars.” From (1) we know all cars are vehicles. From (3) we know no electric cars are gasoline cars, but we don't know about non‑electric cars. Therefore, it’s possible that some cars are gasoline, but we cannot be certain. Conclusion B is not necessarily true. |
| 4 | Analyze Conclusion C | “No cars are gasoline cars.” Statement (3) says no electric cars are gasoline. It does not forbid non‑electric cars from being gasoline. Thus, this conclusion is false. |
| 5 | Analyze Conclusion D | “All vehicles are cars.” Statement (1) says all cars are vehicles, but not vice‑versa. There could be vehicles that are not cars (e.g., bicycles). Hence, Conclusion D is false. |
| 6 | Result | None of the conclusions are necessarily true. The correct answer is None (if allowed) or no conclusion. |
4. Quick Revision Summary
- Statement → Conclusion: infer only what is logically forced by the premises.
- Truth hierarchy: True → True, False → False, Unknown → Uncertain.
- Common inference patterns: modus ponens, modus tollens, hypothetical syllogism.
- Check each conclusion separately; if it can be contradicted, discard it.
- Beware of “some” vs “all” – “All A are B” does not imply “Some A are B” is false; it simply doesn’t guarantee it.
- Always read statements fully; missing a negation can flip the answer.
Practice Tip: Draw a Venn diagram for each problem. Represent sets (e.g., cars, vehicles, electric, gasoline) and shade the regions implied by the statements. Then check which conclusion(s) correspond to the shaded areas.
Good luck with your practice!