Study Notes – “Statement & Conclusion”
(Reasoning Ability – Nagaland TET – Teacher Eligibility)
Goal: Learn how to read a statement, identify the logical relation, and decide whether a conclusion follows necessarily, possibly, not at all, or cannot be determined.
1. Simple Explanation
| Term | Meaning | Example |
|---|---|---|
| Statement | A fact, rule, or condition given in the question. | “All roses are plants.” |
| Conclusion | A claim that must be evaluated against the statement(s). | “All roses are living things.” |
| Inference | The logical step that links the statement to the conclusion. | From “All roses are plants” & “All plants are living things” ⇒ “All roses are living things.” |
Key idea:
A conclusion is necessarily true if it must hold in every possible situation consistent with the statement(s).
If a single counter‑example exists, the conclusion is not necessarily true.
2. Key Points
| # | What to look for | How to use it |
|---|---|---|
| 1. Identify the type of inference | - Deduction (always true) - Induction (likely, but not certain) - Abduction (best explanation) |
For TET, we deal with deductive inference. |
| 2. Check for “necessary” words | e.g., always, never, must, impossible | If the statement uses such words, the conclusion is usually strong. |
| 3. Test with counter‑examples | Assume the statement holds, then try to find a situation where the conclusion fails. | If you can, the conclusion is not necessarily true. |
| 4. Look for hidden premises | Often statements are short. They may rely on common knowledge (e.g., “All mammals are warm‑blooded”). | Bring such knowledge into the inference. |
| 5. Remember the four answer patterns | 1. Necessarily true 2. Possibly true 3. Never true 4. Cannot be determined |
Determine which fits best. |
| 6. Keep the conclusion simple | If the conclusion adds something new that isn’t implied, it’s likely false or indeterminate. | e.g., “All roses are red” (cannot be inferred). |
| 7. Use “contrapositive” test | From “If A then B” → “If not B then not A”. | Helpful for conditional statements. |
3. Worked Example
Statement
- All A's are B's.
- All B's are C's.
- All C's are D's.
Conclusion Choices
| Option | Conclusion | Verdict |
|---|---|---|
| A | Every A is a D. | Necessarily true |
| B | Some A is a D. | Possibly true |
| C | No A is a D. | Never true |
| D | Some B is an A. | Cannot be determined |
Step‑by‑Step Reasoning
-
Chain the statements
All A → B → C → D means every A is a B, every B is a C, and every C is a D.
→ Therefore, every A is a D.
→ Option A is true. -
Option B
“Some A is a D” is weaker than “All A are D”.
Since all A are D, the statement “some A are D” is also necessarily true.
But exam conventions treat “some X” as possibly true unless the statement says all.
So mark it as possibly true. -
Option C
“No A is a D” contradicts the chain. Impossible → never true. -
Option D
“Some B is an A” would require that at least one B is also an A.
The chain only says every A is a B; it does not say every B is an A.
A counter‑example: A = {apple}, B = {apple, banana}.
→ Conclusion cannot be determined.
Quick Checklist
- All A → B & All B → C → All A → C (transitive property).
- Use contrapositive if statement is conditional.
- Test each option with a simple counter‑example.
4. Quick Revision Summary
| Topic | What to Remember |
|---|---|
| **Statement |