Syllogisms

Subject: Reasoning | Frequency: 2-3 questions per APPSC paper | Time: 60-90 sec/question

Introduction

Syllogism questions give two or more premises (statements assumed true) followed by conclusions. You must determine which conclusions logically follow. APPSC favours 2-statement syllogisms with 2 conclusions, including possibility-based questions. The Venn diagram method is the most reliable technique.

Golden Rule: Accept premises as absolutely true. Do NOT use real-world knowledge.

Core Method

1. Draw all possible Venn diagrams for the given statements
2. Check each conclusion against ALL diagrams
3. A conclusion is VALID only if true in ALL possible diagrams
4. If neither follows alone, check complementary pairs for "either-or"

Four Statement Types

Quick Rules

Worked Examples — Easy

Q1: Statements: All dogs are cats. All cats are birds. Conclusions: I. All dogs are birds. II. All birds are dogs.

• Dogs inside cats inside birds → All dogs are birds (valid)
• Birds may contain non-cats → All birds are dogs (invalid)
• Answer: Only I follows

Q2: Statements: Some pens are pencils. All pencils are erasers. Conclusions: I. Some pens are erasers. II. All erasers are pencils.

• Some pens overlap pencils, pencils inside erasers → Some pens are erasers (valid)
• Erasers may contain more than pencils → All erasers are pencils (invalid)
• Answer: Only I follows

Q3: Statements: No apple is a banana. All bananas are cherries. Conclusions: I. No apple is a cherry. II. Some cherries are not apples.

• Apples separate from bananas, bananas inside cherries
• I: Apples might overlap with non-banana cherries → not necessarily true (invalid)
• II: Bananas are cherries but not apples → some cherries are definitely not apples (valid)
• Answer: Only II follows

Worked Examples — Medium

Q4: Statements: All flowers are trees. Some trees are fruits. Conclusions: I. Some flowers are fruits. II. Some fruits are trees.

• Flowers inside trees, some trees overlap fruits
• I: Overlapping trees might not be flowers → not definite (invalid)
• II: Converse of "Some trees are fruits" → always valid
• Answer: Only II follows

Q5: Statements: Some kings are queens. Some queens are jacks. Conclusions: I. Some kings are jacks. II. No king is a jack.

• Two particular statements → no definite conclusion
• I invalid, II invalid
• Complementary pair? "Some kings are jacks" vs "No king is a jack" — YES
• Answer: Either I or II follows

Q6: Statements: All A are B. No B is C. Some C are D. Conclusions: I. No A is C. II. Some D are not B.

• A inside B, B separate from C → A separate from C → No A is C (valid)
• Some C are D, no B is C → those D-containing C's are not B → Some D are not B (valid)
• Answer: Both I and II follow

Worked Examples — Hard

Q7: Statements: All books are pages. Some pages are words. No word is a sentence. Conclusions: I. Some books are not sentences. II. Some pages are not sentences.

• Books inside pages. Some pages are words. Words separate from sentences.
• II: Pages that are words are definitely not sentences → valid
• I: Books might all be in the non-word part of pages → could overlap with sentences → not guaranteed
• Answer: Only II follows

Q8: Statements: No cat is a dog. All dogs are horses. Some horses are cows. Conclusions: I. Some horses are not cats. II. Some cows are not cats.

• Dogs inside horses, dogs separate from cats → some horses (the dog-horses) are not cats → valid
• Cow-horses may or may not overlap with cats → II not guaranteed
• Answer: Only I follows

Q9: Possibility: Statements: Some A are B. All B are C. Conclusion: "All A can be C" — possible?

• Some A are B, B inside C. Remaining A's could also be C.
• Is there a valid diagram where all A are C? Yes (A inside C).
• Answer: Yes, the possibility exists

Shortcuts & Tricks

Common Mistakes

1. Using real-world knowledge — "All dogs are birds" must be accepted as true
2. Drawing only one Venn diagram — must check ALL possible diagrams
3. Missing either-or conclusions — forgetting to check complementary pairs
4. Confusing possible vs definite — "Can be" is different from "Must be"
5. Reversing universal statements — "All A are B" does NOT mean "All B are A"

Exam Strategy

• Master the Venn diagram method — draw 2-3 possible diagrams per problem
• The rules table above eliminates most distractors immediately
• APPSC keeps difficulty at medium; 2-statement problems are standard
• Time: 60-90 seconds per question
• Always check for either-or when both individual conclusions fail
• Negative marking: -0.333 — use the quick rules to be confident

Practice Questions

1. All A are B. All B are C. Conclusion: All A are C? → Follows (A inside B inside C)
2. Some X are Y. No Y is Z. Conclusion: Some X are not Z? → Follows
3. No P is Q. No Q is R. Any conclusion about P and R? → No definite conclusion (two negatives)
4. All men are mortal. Socrates is a man. Conclusion: Socrates is mortal? → Follows
5. Some A are B. Some B are C. Conclusion: Some A are C? → Does not follow (two particulars)

Key Terms / Formulas