Syllogism
About 7 min · General Intelligence and Reasoning · English
Time worked out from the lesson's 489 words at 150 words a minute, plus a minute for each question.
Syllogism tests your ability to draw logical conclusions from two or three statements containing quantifiers like "all," "some," or "no." These problems follow strict formal logic rules—your everyday intuition can mislead you, so mastering the Venn diagram method and formal validity rules is essential.
Key ideas
- Universal affirmative (A): "All X are Y" means every member of X is inside Y. Does not mean all Y are X.
- Universal negative (E): "No X are Y" means X and Y share zero members—completely separate circles in a Venn diagram.
- Particular affirmative (I): "Some X are Y" means at least one member is common. "Some" in logic means "at least one," possibly all.
- Particular negative (O): "Some X are not Y" means at least one member of X lies outside Y.
- Complementary pair (Either-Or): If two conclusions form an A–O, E–I or I–O pair on the same subjects (e.g., "All X are Y" vs "Some X are not Y", or "No X are Y" vs "Some X are Y"), and neither follows individually, then "Either I or II follows" is correct.
Watch out for
- Assuming "Some" means "only some" or "not all": In formal logic, "Some X are Y" allows for the possibility that all X are Y. Students often think "some" excludes "all," leading to wrong negations. Fix: Treat "some" as "at least one, possibly more, possibly all."
- Illegally converting "All A are B" to "All B are A": Conversion of universal affirmatives is invalid. Fix: Only "No" and "Some" statements convert. "All A are B" does not imply "All B are A."
- Combining two negative premises: "No A are B" + "No B are C" yields no valid conclusion about A and C. Fix: Remember two negatives never produce a positive link. Mark "no conclusion" unless an Either-Or applies.
Quick reference
- All/No/Some/Some not — memorise A, E, I, O notation for speed.
- Valid chains: All–All, All–No, Some–All yield conclusions; two particulars or two negatives don't.
- Conversion: Only E and I statements convert validly.
- Either-Or: Use only for complementary pairs when neither follows alone.
- Draw Venn diagrams for tricky cases—visual proof beats intuition.
Check yourself: 3 questions
1. Statements: All dogs are animals. All animals are living beings. Conclusions: I. All dogs are living beings. II. Some living beings are dogs. Which conclusion(s) logically follow(s)?
2. Statements: Some books are pens. No pen is a pencil. Conclusions: I. Some books are not pencils. II. No book is a pencil. Which conclusion(s) logically follow(s)?
3. Statements: All chairs are tables. Some tables are desks. No desk is a bench. Conclusions: I. Some chairs are desks. II. No chair is a bench. Which conclusion(s) logically follow(s)?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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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