Syllogism
About 7 min · Reasoning Ability and Problem Solving · English
Time worked out from the lesson's 525 words at 150 words a minute, plus a minute for each question.
Syllogism is a topic in SSC MTS reasoning. The beauty of syllogism is that once you master the underlying logic and Venn diagram technique, you can solve any question mechanically in under 60 seconds.
Key ideas
- Statements and conclusions: You're given 2–3 categorical statements (premises) and 3–4 possible conclusions. Your task is to determine which conclusions logically follow from the statements alone, ignoring real-world facts.
- Four standard statement types: (1) Universal affirmative "All A are B" — complete inclusion, (2) Universal negative "No A are B" — complete exclusion, (3) Particular affirmative "Some A are B" — at least partial overlap, (4) Particular negative "Some A are not B" — at least partial non-overlap.
- Venn diagram method: Draw circles for each category. "All A are B" means A-circle entirely inside B-circle. "No A are B" means separate circles. "Some A are B" means overlapping circles. This visual technique eliminates guesswork.
- Complementary pair rule: In SSC exams, if two conclusions form a complementary pair ("Some A are B" and "Some A are not B" OR "All A are B" and "Some A are not B"), and neither follows individually but together they cover all cases, then "either-or follows" is the answer.
- "Some" means at least one: In logic, "Some A are B" means at least one A is B, possibly all. It does NOT mean "only a few." This misunderstanding causes many wrong answers.
Watch out for
- Applying real-world logic → Ignore reality: Students reject "All rivers are mountains" as absurd. Wrong. Treat statements as hypothetical universes. Real-world knowledge must not influence your answer.
- Misreading "Some" as "only some, not all" → "Some" includes the possibility of "all": In logic, "Some A are B" is true even if all A are B. Don't exclude the universal case.
- Assuming possibilities are certainties → Only definite conclusions count: If a conclusion might be true, it doesn't follow. A Venn diagram showing two possible arrangements where one makes the conclusion false means the conclusion doesn't follow.
Quick reference
- Draw Venn diagrams for every syllogism — visual beats mental juggling.
- All + All = definite conclusion; All + Some = usually no conclusion.
- "Some" reverses freely: Some A are B = Some B are A.
- Two negative statements never give a conclusion.
- Complementary pair: Some are / Some are not → Either-or follows if neither alone is certain.
Check yourself: 3 questions
1. Statements: All books are papers. All papers are files. Conclusions: I. All books are files. II. Some files are books. Which conclusion(s) logically follow(s)?
2. Statements: Some cats are dogs. No dog is a bird. Conclusions: I. Some cats are not birds. II. No cat is a bird. Which conclusion(s) logically follow(s)?
3. Statements: All managers are employees. Some employees are engineers. All engineers are graduates. Conclusions: I. Some graduates are managers. II. Some graduates are employees. Which conclusion(s) logically follow(s)?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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