📚 Delhi TET – Reasoning Ability
Topic: Statement & Conclusion
In the Statement & Conclusion section, the exam‑taker is given a short statement (premise) followed by two conclusions.
The task is to decide which conclusion logically follows from the statement.
1️⃣ Simple Explanation
| Term | Meaning |
|---|---|
| Statement (Premise) | A fact or observation about a situation. |
| Conclusion | An inference that can be drawn logically from the statement. |
| Inference | The process of deriving a conclusion from a premise. |
Rule of thumb:
A conclusion is valid if it necessarily follows from the statement.
If the statement gives enough information to guarantee the conclusion, it is correct.
2️⃣ Key Points to Remember
| Category | Important Items |
|---|---|
| Logical Connectives | AND, OR, IF…THEN, NOT, SOME, ALL, NO |
| Types of Inferences | • Universal (All A are B) → (All A are B) • Particular (Some A are B) → (Some A are B) • Contrapositive (If B then A) → (If not A then not B) |
| Common Pitfalls | • Assuming all are covered by “some” statements. • Confusing “some” with “all”. • Ignoring negative words (“not”, “never”). |
| Checking Steps | 1. Write the statement in propositional form. 2. Translate each conclusion. 3. See if the conclusion is a logical consequence. |
| Time Management | 10–15 s per question. Focus on key words: all, some, none, any, every. |
3️⃣ Worked Example
Statement (S):
“All teachers in the school are senior staff. Some senior staff are not qualified teachers.”
Step‑by‑Step
| Step | Action | Reasoning |
|---|---|---|
| 1 | Translate the statement | Let: - (T(x)): “(x) is a teacher” - (S(x)): “(x) is a senior staff” - (Q(x)): “(x) is a qualified teacher” S1: ∀x ( (T(x) \rightarrow S(x)) ) S2: ∃x ( (S(x) \land \neg Q(x)) ) |
| 2 | Write the two conclusions | C1: Some teachers are not qualified teachers. C2: All senior staff are teachers. |
| 3 | Translate conclusions | C1: ∃x ( (T(x) \land \neg Q(x)) ) C2: ∀x ( (S(x) \rightarrow T(x)) ) |
| 4 | Check C1 | From S1 we know every teacher is senior staff. S2 gives at least one senior staff who is not a qualified teacher. That person could be a teacher or not. But we cannot guarantee that the non‑qualified senior staff is a teacher. So C1 is not a necessary consequence. |
| 5 | Check C2 | S1 tells us that all teachers are senior staff, but it does not say that all senior staff are teachers. Hence C2 is also not a necessary consequence. |
| 6 | Result | Neither conclusion follows. |
Answer: None of the above (if that option exists) – otherwise both C1 and C2 are invalid.
4️⃣ Quick Revision Summary
| Check | What to look for | Quick Tip |
|---|---|---|
| Universal → Universal | “All A are B” → “All A are B” | ✔️ |
| Universal → Particular | “All A are B” → “Some A are B” | ✔️ |
| Particular → Universal | “Some A are B” → “All A are B” | ❌ |
| Contrapositive | “If A then B” → “If not B then not A” | ✔️ |
| Negation | “No A are B” → “All A are not B” | ✔️ |
| Mixed quantifiers | “Some A are not B” & “All B are C” → “Some A are not C” | ✔️ |
| Beware of “some” | “Some A are B” does not mean “All A are B”. | ❌ |
| Key words | All, Every, Every A is B → universal. Some, Any, At least one → particular. None, No → universal negation. |
📌 Final Practice Question
Statement: “All engineers are problem solvers. Some problem solvers are not mathematicians.”
Conclusion 1: Some engineers are not mathematicians.
Conclusion 2: All problem solvers are engineers.
Which conclusion(s) follow?
Try solving on your own before checking the answer!
📚 Final Words
- Convert the statement and conclusions into clear logical form.
- Use the universal and particular rules to test each conclusion.
- Remember that “some” does not imply “all”.
- A quick mental check: If the conclusion would be false when the statement is true, then it’s invalid.
Good luck with your preparation for the Delhi TET!