RBI Grade‑B – Reasoning Ability
Topic: Statement & Conclusion
In a Statement‑and‑Conclusion (S‑C) question you’re given a set of statements (facts) and a list of conclusions.
Your job is to decide which conclusions are necessarily true given the statements.
Only conclusions that are true in every possible scenario that satisfies the statements are correct.
1. Simple Explanation
| Term | Meaning | Example |
|---|---|---|
| Statement | A fact or set of facts about a situation. | “All cats are mammals.” |
| Conclusion | A proposition that may or may not follow from the statements. | “All mammals are cats.” |
| Valid Conclusion | A conclusion that is logically entailed by the statements – it must be true no matter how the universe that satisfies the statements looks. | From “All cats are mammals” and “All mammals are animals” we can validly conclude “All cats are animals.” |
| Invalid Conclusion | A conclusion that may be false in some possible universe that satisfies the statements. | From the same two statements we cannot conclude “Some cats are animals.” (Because “all” implies “some”, but the question tests necessity, not possibility.) |
Key Idea – Never assume the universe is non‑empty unless the statement explicitly says so. If a statement says “All X are Y”, you cannot automatically assume that X is non‑empty.
Therefore a conclusion that requires the existence of at least one X (e.g., “Some X are Y”) is not guaranteed unless the statements say X is non‑empty.
2. Key Points / Rules of Thumb
| # | Rule | Why it matters | Example |
|---|---|---|---|
| 1. Universal → Universal | “All A are B” & “All B are C” ⇒ All A are C | Transitivity of universal statements. | All students are learners. All learners are humans. ⇒ All students are humans. |
| 2. Universal + Particular | “All A are B” & “Some B are C” ⇒ Cannot conclude about A and C. | Particularity breaks the chain. | All dogs are mammals. Some mammals are whales. ⇒ We cannot say anything about dogs & whales. |
| 3. Particular + Particular | “Some A are B” & “Some B are C” ⇒ Cannot conclude about A and C. | The overlap may be different. | Some students are doctors. Some doctors are teachers. ⇒ We cannot say any student is a teacher. |
| 4. Universal + Negative | “No A are B” & “All B are C” ⇒ No A are C | Negative relation propagates. | No cats are reptiles. All reptiles are cold‑blooded. ⇒ No cats are cold‑blooded. |
| 5. Double Negatives | “No A are B” & “No B are C” ⇒ Cannot conclude about A and C. | They may belong to disjoint sets. | No birds are fish. No fish are mammals. ⇒ We cannot say anything about birds & mammals. |
| 6. “All” vs “Some” | From “All A are B” you can deduce “Some A are B” only if A is non‑empty. | Usually RBI assumes the set is non‑empty if it’s mentioned. | All roses are flowers. ⇒ Some roses are flowers only if roses exist. |
| 7. “Some” → “Some” | “Some A are B” ⇒ Some B are A (symmetry of the particular statement). | The relation is reciprocal. | Some architects are engineers. ⇒ Some engineers are architects. |
| 8. “No” → “No” | “No A are B” ⇒ No B are A. | Symmetry of the negative statement. | No politicians are teachers. ⇒ No teachers are politicians. |
| 9. “All” + “No” | “All A are B |