UP Police Constable · Bite-size lessons
Syllogism
About 7 min · Mental Aptitude / IQ / Reasoning · English
Time worked out from the lesson's 582 words at 150 words a minute, plus a minute for each question.
Syllogism is a fundamental reasoning topic in the UP Police Constable exam where you must draw logical conclusions from given statements involving categorical propositions using terms like "All", "Some", "No" and "Some not". This topic tests your ability to think logically without relying on general knowledge or real-world truth — you must accept the given statements as true even if they contradict reality (e.g., "All dogs are cats" must be treated as true within the question context).
Key ideas
- Categorical Propositions: Statements are structured as "All A are B", "No A are B", "Some A are B", or "Some A are not B". These four forms are the building blocks of all syllogism problems.
- Absolute Truth: Within syllogism, given statements are considered absolutely true regardless of real-world validity. The conclusion must follow from the logical structure alone, not from factual correctness.
- Venn Diagram Method: Drawing overlapping circles for each category helps visualize all possible relationships. This visual approach prevents logical errors and makes complex statements manageable.
- Distribution of Terms: In "All A are B", term A is distributed (completely contained) but B is not. In "No A are B", both terms are distributed. Understanding distribution helps apply formal logic rules correctly.
- Complementary Pairs: "All" and "Some not" form one complementary pair; "No" and "Some" form another. If "All A are B" is false, then "Some A are not B" must be true, and vice versa.
Watch out for
- Applying Real-World Knowledge: Students reject "All cars are buses" as a valid statement because it's factually false. Wrong approach → Accept all given statements as true within the question; ignore real-world facts.
- Assuming "All A are B" means "All B are A": This is the most common error. "All chairs are furniture" does not mean "All furniture are chairs". Correct fix → Always draw Venn diagrams; smaller set goes inside larger set, not vice versa.
- Ignoring Multiple Venn Possibilities: For "Some A are B", students draw only one diagram (partial overlap) and miss complete overlap case where all A inside B. Correct fix → For "Some" statements, consider all possible valid configurations: partial overlap, A inside B, or B inside A.
Quick reference
- Venn diagrams are mandatory — draw circles for every term in statements to avoid logical errors.
- All → Some conversion always valid: "All A are B" always implies "Some B are A" and "Some A are B".
- All + No = No; No + All = Some not (reversed): When one statement is negative (No) and other is universal (All), conclusion is negative.
- Some + Some = No definite conclusion: Two particular statements never yield certainty, only possibility.
- Accept absurd statements as true — logic structure matters, not real-world truth.
Check yourself: 3 questions
1. Statements: All flowers are plants. All plants are living things. Conclusions: I. All flowers are living things. II. Some living things are flowers. Which conclusion(s) logically follow?
2. Statements: Some books are pens. All pens are pencils. Conclusions: I. Some books are pencils. II. All pencils are books. Which conclusion(s) logically follow?
3. Statements: No dog is a cat. Some cats are animals. Conclusions: I. Some animals are not dogs. II. No cat is a dog. Which conclusion(s) logically follow?
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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