📚 Study Notes – Reasoning Ability: Statement & Conclusion
(For Himachal Pradesh TET – Teacher Eligibility Test)
Why this topic matters
In TET Reasoning, you’ll often encounter questions where you have to judge whether a given Conclusion follows logically from one or more Statements. Mastering this will boost your accuracy in the “Statement & Conclusion” section.
1. Simple Explanation
| Term | What it is | Example |
|---|---|---|
| Statement (S) | A proposition or fact that is given. | “All dogs have four legs.” |
| Conclusion (C) | A proposition that is derived from the statement(s). | “All four‑legged animals are dogs.” |
Goal: Determine if the conclusion is necessarily true when the statement(s) are true.
- Valid → conclusion must always be true if the statements are true.
- Invalid → conclusion may be false even if the statements are true.
2. Key Points
| # | Concept | How to Apply in TET |
|---|---|---|
| 1 | Universal vs. Particular | Distinguish between All / No (universal) and Some / Some (not) (particular). |
| 2 | Direction of inference | You can infer forward (S → C) or backwards (C → S) only if the logic is sound. |
| 3 | Transitive Property | If A → B and B → C, then A → C is valid. |
| 4 | Contrapositive | From If A then B, you cannot automatically conclude If not B then not A (unless A → B is necessary). |
| 5 | Syllogism | Standard categorical syllogisms (AAA‑1, EAE‑1, etc.) follow classical rules. |
| 6 | Non‑Contradictory | Statements must not conflict; otherwise, any conclusion is moot. |
| 7 | Type of Question |
- S‑C: One statement → one conclusion.
- S‑C‑S: One statement → conclusion → another statement.
- S‑S‑C: Two statements → one conclusion. | | 8 | Check for Over‑generalization | Conclusion must not be more general than the premises unless logically implied. | | 9 | Language Clues | Words like all, none, any, some, every are key. |
3. Worked Example
Question
Statement 1 (S1): All birds can fly.
Statement 2 (S2): Some penguins are birds.
Conclusion (C): Some penguins can fly.
Is the conclusion valid?
Step‑by‑Step Solution
| Step | Reasoning | Verdict |
|---|---|---|
| 1 | Translate S1: ∀x (Bird(x) → Fly(x)) | |
| 2 | Translate S2: ∃x (Penguin(x) ∧ Bird(x)) | |
| 3 | From S1, any bird flies. | So for any x that is a penguin & bird, x flies. |
| 4 | S2 guarantees the existence of at least one such x. | Therefore at least one penguin flies. |
| 5 | Conclusion C states: ∃x (Penguin(x) ∧ Fly(x)) | Matches the deduction. |
| 6 | Conclusion is valid. | ✔️ |
Common Pitfall
Many students think the conclusion is invalid because “penguins can’t fly”, but that is a fact, not a logical implication from the given statements. In reasoning tests, you judge based solely on the provided statements, not external knowledge.
4. Quick Revision Summary
| ✔️ | ✅ | ❌ |
|---|---|---|
| ✓ Identify S and C. | ✓ Use universal & particular quantifiers. | ❌ Assume real‑world facts that aren’t in the statements. |
| ✓ Apply transitivity (A→B, B→C ⇒ A→C). | ✓ Avoid over‑generalization. | ❌ Infer backwards unless logically justified. |
| ✓ Check for contradictory statements first. | ✓ Recognize syllogistic patterns (AAA‑1, EAE‑1, etc.). | ❌ Mix up all with some or no with not. |
| ✓ Practice S‑C, S‑C‑S, S‑S‑C formats. | ✓ Memorize key logical rules in a quick‑look table. | ❌ Skip the “quick look” step; it’s the best revision tool. |
Final Tips
- Read Carefully – Pay attention to words like any, all, none, some.
- Sketch a Quick Diagram – For S‑S‑C, draw a V