Statement-Conclusion

Statement-Conclusion

🟢 Lite

Key Pattern/Rule

Only conclusions that are logically necessary from the given statements are valid — never assume what isn’t directly supported.

Memory Trick

Think of statements as “facts” and conclusions as “the only possible truth.” If you can imagine the statements being true but the conclusion being false, it’s NOT valid.

1-Sentence Summary

Tests your ability to deduce what MUST be true from given premises without adding your own assumptions.

Quick Example

Q: All roses are flowers. Some flowers are red. Conclusion: Some roses are red. A: Cannot be determined — “Some flowers are red” doesn’t tell us which flowers, so roses may or may not be among them.

Quick Example 2

Q: No cat is a dog. All dogs are animals. Conclusion: No cat is an animal. A: Invalid — dogs are animals but cats aren’t dogs, so cats could still be animals. The statement doesn’t rule it out.

🟡 Standard

Concept

Statement-Conclusion questions give you a set of premises (statements) and ask you to determine which conclusion logically follows. The golden rule: a valid conclusion must be definitely true — not probably true, not possibly true, but the only option given the information.

GATE loves testing your ability to avoid assumptions. Just because something “makes sense” doesn’t mean it follows logically. You need to check every possible arrangement consistent with the statements and see if the conclusion holds in all of them.

The statements usually involve categorical relationships: “All A are B,” “Some A are B,” “No A is B,” or “Some A are not B.” Each of these creates different logical constraints, and combining them requires careful reasoning.

Types & Approach

Type 1: All/Some Conversions

• “All A are B” → “Some B are A” (valid conversion)
• “No A is B” → “No B is A” (valid both ways)
• “Some A are B” ↔ “Some B are A” (valid)
• “Some A are not B” — no direct conversion

Type 2: Transitive Relations Chain relationships together: if All A are B, and All B are C, then All A are C. Watch out: “Some” doesn’t transit easily. “Some A are B” + “Some B are C” tells us nothing about A and C.

Type 3: Either-Or Conclusions If one conclusion must be true and the other must be false, you get an either-or situation. This often happens with complementary pairs like “All X are Y” vs “Some X are not Y.”

Step-by-Step Example

Q: Statements:

1. All teachers are educated.
2. Some educated people are patient.
3. No patient people are rude.

Conclusions:

1. Some teachers are patient.
2. No teacher is rude.

Approach: Step 1 → Draw what you know: Teachers ⊂ Educated. Some Educated ∩ Patient. Patient ∩ Rude = ∅. Step 2 → Check Conclusion 1: Can some teachers be patient? Yes — teachers are educated, and some educated are patient, so it’s possible but not definite. Invalid (not necessarily true). Step 3 → Check Conclusion 2: Statement 3 only forbids patient people from being rude; equivalently, every rude person is non-patient. It says nothing about teachers who are not patient. Since teachers need not be patient, a teacher can be both rude and non-patient without contradicting any statement. So “No teacher is rude” need not hold. Invalid.

Answer: Neither conclusion follows.

Common Mistakes

• Assuming what “makes sense” rather than what logically follows → Always verify by asking “Can I imagine the statements true and this conclusion false?”
• Mixing up “Some” with “All” → “Some” just means “at least one,” not a quantity.
• Forgetting that “absence of information” is not the same as “negative information” → Just because something isn’t stated doesn’t mean it’s denied.

🔴 Extended

Full Concept Explanation

Statement-Conclusion is one of the most conceptually tricky topics in Logical Reasoning because it forces you to abandon everyday intuition and embrace strict logical necessity. In real life, we often reason probabilistically — “probably this is true, so I’ll act on it.” GATE demands something stricter: certainty or rejection, no middle ground.

The fundamental principle is this: a conclusion follows from premises if and only if the conclusion is true in every possible scenario consistent with those premises. If you can construct even one scenario where the premises hold but the conclusion doesn’t, the conclusion is invalid. This is called the “counterexample method,” and it’s your best tool for these questions.

When dealing with categorical statements, memorize the logical relationships:

• All A are B: A is a subset of B. Every element in A is also in B.
• Some A are B: The intersection of A and B contains at least one element.
• No A is B: A and B are disjoint sets — no common elements.
• Some A are not B: At least one element of A is outside B. This is weaker than “All A are B” being false — it could be that some are in B, some aren’t.

The conversion rules matter: “All A are B” logically implies “Some B are A” (because if all A is in B, then at least one A exists in B, which means some B is A). But be careful — “All A are B” does NOT mean “Only A are B” (that’s an unwarranted quantifier shift). Similarly, “Some A are B” does NOT mean “Some A are not B” — both could be true simultaneously.

Negation handling is critical. The negation of “All A are B” is “Some A are not B” (not “No A is B”). These are contradictories — exactly one must be true. “No A is B” and “Some A are B” are also contradictories. Getting negation wrong will destroy your accuracy on these questions.

GATE-Level Practice

Q1: Statements:

1. All parks are quiet.
2. No quiet places are crowded.
3. Some crowded places have lights.

Conclusions:

1. No park is crowded.
2. Some parks have lights.

Answer: Conclusion 1 follows (All parks are quiet, no quiet place is crowded → parks aren’t crowded). Conclusion 2 does not follow — we can’t connect parks to lights from the given statements.

Q2: Statements:

1. Some artists are dreamers.
2. All dreamers are imaginative.
3. No imaginative people are realistic.

Conclusions:

1. Some artists are not imaginative.
2. No dreamer is realistic.
3. All artists are imaginative.

Answer: Conclusion 1 is invalid (some artists are dreamers and all dreamers are imaginative, so some artists ARE imaginative — doesn’t mean any aren’t). Conclusion 2 follows (all dreamers are imaginative, no imaginative are realistic → no dreamer is realistic). Conclusion 3 is invalid — “some artists are dreamers” doesn’t mean ALL artists are dreamers.

Multiple Approaches

Standard Method: Translate statements to logical constraints, list all possible arrangements, check if conclusion holds in all.

Shortcut — Venn Diagram: Draw overlapping circles for each category. Fill in what you know. If the conclusion’s region is definitely filled, it follows; if it’s definitely empty, it follows (as a negation); if it could go either way, it doesn’t follow.

Counterexample Hunt: When unsure, try to construct a scenario where premises are true and the conclusion is false. If you can, the conclusion doesn’t follow.

Tricky Cases / Edge Cases

• “At least one” doesn’t mean “only one”: “Some A are B” allows the possibility that ALL A are B. Don’t assume exclusivity.
• The “some not” trap: “Some A are not B” tells you nothing about the relationship between the remaining portion of A and B. They could all be in B or none could.
• Complementary pairs: When conclusions are presented as either-or (one must be true), check if they’re logical complements. “All X are Y” and “Some X are not Y” cannot both be true — exactly one is true.
• Undeclared existence: “All unicorns are pink” is technically true if no unicorns exist (vacuous truth). In most GATE contexts, assume categories have at least one member unless stated otherwise.

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