Statement and Conclusion — RRB NTPC Study Notes

Overview

Statement and Conclusion questions test your ability to draw logically valid inferences from given information. In RRB NTPC, you'll typically see 1–2 statements followed by 2–4 possible conclusions, and you must identify which conclusions **logically follow** from the statements. This is not about whether the conclusion is factually true in the real world—it's about whether the conclusion can be validly derived from what's stated, assuming the statements are true.

This topic appears in 2–4 questions per paper and overlaps conceptually with syllogisms and analytical reasoning. Mastery requires distinguishing between what is explicitly stated, what can be logically inferred, and what requires assumptions beyond the given information. Students often lose marks by bringing real-world knowledge into purely logical problems or by confusing "follows logically" with "sounds reasonable."

The key skill is strict logical thinking: treat statements as absolutely true, ignore outside knowledge, and apply inference rules mechanically. Practice speeds up pattern recognition for common conclusion structures.

Key Concepts

• **Statement**: A declarative sentence assumed to be true for the purpose of the question. You must accept it as given, even if it contradicts reality.

• **Conclusion**: A proposition that may or may not follow logically from the statement(s). A conclusion "follows" if it must be true whenever the statements are true.

• **Logical Following vs. Possibly True**: A conclusion follows only if the statements **guarantee** it. If a conclusion could be true or could be false based on the statements, it does **not** follow.

• **Definite vs. Probable**: Conclusions using words like "all," "no," "definitely" make strong claims. Conclusions with "some," "may," "possibly" make weaker claims. Weaker claims are easier to satisfy but still must be logically supported.

• **Complementary Pairs**: If one conclusion says "All X are Y" and another says "Some X are not Y," both cannot follow simultaneously. Watch for mutually exclusive conclusion pairs.

• **Implicit Information**: Sometimes a statement implies additional facts through logical necessity (e.g., "All cats are animals" implies "Some animals are cats"), but you cannot add information not implied by the statements.

• **Common Question Formats**: (a) Only conclusion I follows. (b) Only conclusion II follows. (c) Either I or II follows. (d) Neither I nor II follows. (e) Both I and II follow.

• **"Either-Or" Case**: When two conclusions are complementary (one must be true if the statements are true, but you can't tell which), the answer is "Either I or II follows." This is rare and specific.

Formulas / Key Facts

1. **Universal Affirmative (All X are Y)**: Implies "Some Y are X" and "Some X are Y." Does NOT imply "All Y are X."

2. **Universal Negative (No X are Y)**: Implies "No Y are X" and "Some X are not Y" and "Some Y are not X."

3. **Particular Affirmative (Some X are Y)**: Implies "Some Y are X." Does NOT imply anything about "all."

4. **Particular Negative (Some X are not Y)**: Does NOT imply "No X are Y." Leaves room for some X to be Y.

5. **Conversion Rule**: "All X are Y" does NOT convert to "All Y are X." But "No X are Y" converts to "No Y are X," and "Some X are Y" converts to "Some Y are X."

6. **Negation**: If "All X are Y" is given, you cannot conclude "Some X are not Y." If "Some X are Y" is given, you cannot conclude "No X are Y."

7. **Chain Rule**: "All A are B" and "All B are C" together imply "All A are C." Works for universal statements, not for "some" statements without additional logic.

8. **Complementary Conclusions**: "All X are Y" and "Some X are not Y" are complementary; exactly one must be true in reality, but neither may follow from ambiguous statements.

Worked Examples

**Example 1:** **Statement:** All books are papers. All papers are sheets. **Conclusions:** I. All books are sheets. II. Some sheets are books.

**Solution:**

• From "All books are papers" and "All papers are sheets," we apply the chain rule: All books → papers → sheets. So "All books are sheets" follows. Conclusion I follows.
• "All books are sheets" implies "Some sheets are books" (because at least the books are among the sheets). Conclusion II follows.
• **Answer:** Both I and II follow.

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**Example 2:** **Statement:** Some doctors are engineers. No engineer is a pilot. **Conclusions:** I. Some doctors are pilots. II. Some doctors are not pilots.

**Solution:**

• "Some doctors are engineers" and "No engineer is a pilot" means those doctors who are engineers cannot be pilots. So at least some doctors (the engineer ones) are definitely not pilots. Conclusion II follows.
• We have no information about doctors who are not engineers—they might or might not be pilots. We cannot conclude "Some doctors are pilots." Conclusion I does not follow.
• **Answer:** Only conclusion II follows.

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**Example 3:** **Statement:** Some cats are dogs. **Conclusions:** I. All cats are dogs. II. Some cats are not dogs.

**Solution:**

• "Some cats are dogs" means at least one cat is a dog. It does NOT mean all cats are dogs. Conclusion I does not follow.
• "Some" leaves the status of other cats undetermined. The statement doesn't rule out that all cats could be dogs (just says at least one is). So we cannot conclude "Some cats are not dogs." Conclusion II does not follow.
• **Answer:** Neither I nor II follows.

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Common Mistakes

• **Bringing Real-World Knowledge**: Mistake—Rejecting "All pens are elephants" because it's absurd. Fix—Treat every statement as true within the problem universe; logic doesn't care about real-world plausibility.

• **Confusing "Some" with "Only Some"**: Mistake—Thinking "Some X are Y" means "Some X are not Y." Fix—"Some" means "at least one," not "only a few." It allows for the possibility that all X are Y.

• **Assuming Converse Statements**: Mistake—From "All A are B," concluding "All B are A." Fix—Universal affirmatives do not convert. Only conclude what the direction of implication allows.

• **Ignoring Chain Logic**: Mistake—Failing to combine two statements like "All A are B" and "All B are C." Fix—Always check if statements link together to form a transitive chain.

• **Marking "Either-Or" Incorrectly**: Mistake—Choosing "Either I or II" when both conclusions independently follow or when neither follows. Fix—"Either-or" applies only when conclusions are complementary pairs and statements guarantee one but not which one.

Quick Reference

• Accept all statements as true; ignore real-world facts.
• "All X are Y" → "Some Y are X," but NOT "All Y are X."
• "Some X are Y" → "Some Y are X," does NOT imply "Some X are not Y."
• Chain universal statements: All A→B, All B→C ⇒ All A→C.
• Complementary conclusions: if one must be true but you can't tell which, answer "Either-or."
• Read conclusions carefully—"All" vs. "Some" vs. "No" changes everything.