Syllogism
About 6 min · Reasoning Ability · English
Time worked out from the lesson's 397 words at 150 words a minute, plus a minute for each question.
Syllogism is a core logical reasoning topic that tests your ability to draw valid conclusions from given statements.
Key ideas
- Accept statements as absolutely true: Never question whether "All cats are dogs" makes real-world sense. If the statement says it, believe it for that problem.
- Four standard statement types (A, E, I, O):
- "Some" means "at least one": It could mean one, many, or even all. "Some X are Y" doesn't exclude the possibility that all X are Y.
- "Some X are Y" implies "Some Y are X": This is called converse. Particular affirmatives are convertible.
- "No X is Y" implies "No Y is X": Universal negatives are also fully convertible.
Watch out for
- Assuming "All X are Y" means "All Y are X" → Wrong! "All cats are animals" doesn't mean "All animals are cats." Always convert universal affirmative to particular only.
- Applying real-world logic → "All dogs are cats" feels false, so students ignore it. Treat every statement as hypothetically true for that problem.
- Forgetting "Some" includes "All" → If "All X are Y," then "Some X are Y" is automatically true. Don't mark it as "doesn't follow."
Quick reference
- A = All X are Y | E = No X is Y | I = Some X are Y | O = Some X are not Y
- Convertible fully: E and I | Convertible to particular: A | Not convertible: O
- Two particulars = No conclusion | Two negatives = No conclusion
- "Some" includes the possibility of "All"
- Complementary pair: "Some are" + "Some are not" — one must always be true
Check yourself: 3 questions
1. Statements: All books are pages. All pages are words. Conclusions: I. All books are words. II. Some words are books. Which conclusion logically follows?
2. Statements: Some doctors are engineers. All engineers are scientists. Conclusions: I. Some doctors are scientists. II. All doctors are scientists. Which conclusion logically follows?
3. Statements: All flowers are trees. No tree is a fruit. Some fruits are vegetables. Conclusions: I. No flower is a fruit. II. Some vegetables are not trees. Which conclusion logically follows?
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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