Syllogism

Key Concepts & Formulas

Provide 5-7 essential concepts for Syllogism:

10 Practice MCQs

Generate 10 MCQs with increasing difficulty (Q1-3: Easy, Q4-7: Medium, Q8-10: Hard)

Q1. Statements: All trains are vehicles. All vehicles have wheels. Conclusions: I. All trains have wheels. II. Some vehicles are trains. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: C) Both follow

Solution: Draw two concentric circles: Trains ⊂ Vehicles ⊂ Wheels

• Conclusion I: Trains → Wheels (True, as trains ⊂ vehicles ⊂ wheels)
• Conclusion II: Vehicles → Trains (True, as trains ⊂ vehicles, so some vehicles are trains)

Shortcut: If A⊂B⊂C, then A⊂C and B∩A=A

Concept: Syllogism - Transitive property

Q2. Statements: Some stations are junctions. No junction is a terminal. Conclusions: I. Some stations are not terminals. II. No terminal is a junction. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: C) Both follow

Solution: Draw overlapping circles: Stations ∩ Junctions ≠ ∅, Junctions ∩ Terminals = ∅

• Conclusion I: Some stations (those that are junctions) are not terminals (True)
• Conclusion II: If no junction is terminal, then no terminal is junction (True, same statement reversed)

Shortcut: “No A is B” = “No B is A”

Concept: Syllogism - Complementary statements

Q3. Statements: All express trains are fast. Some fast trains are superfast. Conclusions: I. Some express trains are superfast. II. All superfast are fast. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: A) Only I follows

Solution: Express ⊂ Fast, Fast ∩ Superfast ≠ ∅

• Conclusion I: Possible (express trains could be in the intersection)
• Conclusion II: Not necessarily (some superfast could be outside fast)

Shortcut: “Some” allows possibility, doesn’t guarantee

Concept: Syllogism - Possibility vs certainty

Q4. Statements: All platforms are long. Some platforms are crowded. No crowded place is safe. Conclusions: I. Some long things are not safe. II. Some crowded platforms are long. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: C) Both follow

Solution: Platform ⊂ Long, Platform ∩ Crowded ≠ ∅, Crowded ∩ Safe = ∅

• Conclusion I: Some long things (crowded platforms) are not safe (True)
• Conclusion II: Some crowded platforms are long (True, as all platforms are long)

Shortcut: Combine statements: Platform → Long AND Platform ∩ Crowded → Long ∩ Crowded

Concept: Syllogism - Multiple statement combination

Q5. Statements: Some tickets are reserved. All reserved tickets are expensive. No expensive ticket is available. Conclusions: I. Some tickets are not available. II. No reserved ticket is available. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: C) Both follow

Solution: Ticket ∩ Reserved ≠ ∅, Reserved ⊂ Expensive, Expensive ∩ Available = ∅

• Conclusion I: Some tickets (reserved ones) are expensive and thus not available (True)
• Conclusion II: Reserved ⊂ Expensive ⊂ Not Available (True)

Shortcut: Chain: A∩B ⊂ C ⊂ D → A∩B ⊂ D

Concept: Syllogism - Extended chain reasoning

Q6. Statements: All drivers are employees. Some employees are graduates. No graduate is illiterate. Conclusions: I. Some drivers are graduates. II. No employee is illiterate. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: D) Neither follows

Solution: Driver ⊂ Employee, Employee ∩ Graduate ≠ ∅, Graduate ∩ Illiterate = ∅

• Conclusion I: Not necessarily (drivers could be outside graduate circle)
• Conclusion II: Not necessarily (non-graduate employees could be illiterate)

Shortcut: Check if conclusion MUST be true in all possible arrangements

Concept: Syllogism - Non-mandatory conclusions

Q7. Statements: Some mail trains are delayed. All delayed trains are late. Some late trains are cancelled. Conclusions: I. Some mail trains are late. II. Some cancelled trains are mail trains. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: A) Only I follows

Solution: Mail ∩ Delayed ≠ ∅, Delayed ⊂ Late, Late ∩ Cancelled ≠ ∅

• Conclusion I: Mail → Delayed → Late (True)
• Conclusion II: Not necessarily (cancelled trains could be from different category)

Shortcut: First conclusion in chain always follows if A∩B ⊂ C

Concept: Syllogism - Chain conclusion validity

Q8. Statements: All AC coaches are comfortable. Some comfortable coaches are expensive. No expensive coach is economical. Conclusions: I. Some AC coaches are not economical. II. No comfortable coach is economical. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: A) Only I follows

Solution: AC ⊂ Comfortable, Comfortable ∩ Expensive ≠ ∅, Expensive ∩ Economical = ∅

• Conclusion I: Possible (AC coaches could be in expensive subset)
• Conclusion II: Not necessarily (comfortable coaches could be economical if not expensive)

Shortcut: Check if subset relationship forces the conclusion

Concept: Syllogism -Subset possibility analysis

Q9. Statements: Some passengers are daily travelers. All daily travelers have passes. Some pass holders are not season ticket holders. Conclusions: I. Some passengers are not season ticket holders. II. Some daily travelers are not season ticket holders. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: C) Both follow

Solution: Passenger ∩ Daily ≠ ∅, Daily ⊂ Pass, Pass ∩ ¬Season ≠ ∅

• Conclusion I: Some passengers (daily travelers) have passes, and some pass holders are not season ticket holders (True)
• Conclusion II: Daily travelers ⊂ Pass, and some pass holders are not season ticket holders (True)

Shortcut: If A∩B ⊂ C and C∩¬D ≠ ∅, then A∩B∩¬D possible

Concept: Syllogism - Complex subset analysis

Q10. Statements: All local trains stop at all stations. Some trains that stop at all stations are passenger trains. No passenger train is a superfast train. Conclusions: I. Some local trains are not superfast trains. II. All trains that stop at all stations are local trains. A) Only I follows B) Only II follows C) Both follow D) Neither follows

Answer: A) Only I follows

Solution: Local ⊂ Stop-all, Stop-all ∩ Passenger ≠ ∅, Passenger ∩ Superfast = ∅

• Conclusion I: Local ⊂ Stop-all ⊂ ¬Superfast (True)
• Conclusion II: Not necessarily (passenger trains also stop at all stations)

Shortcut: Check if subset relationship is bidirectional

Concept: Syllogism - One-way vs two-way relationships

5 Previous Year Questions

Generate PYQ-style questions with authentic exam references:

PYQ 1. Statements: All birds are animals. Some animals are humans. Conclusions: I. Some birds are humans. II. All humans are animals. [RRB NTPC 2021 CBT-1]

Answer: D) Neither follows

Solution: Bird ⊂ Animal, Animal ∩ Human ≠ ∅

• Conclusion I: Not necessarily (birds could be outside human circle)
• Conclusion II: Not necessarily (only some animals are humans)

Exam Tip: “Some” statements don’t allow “All” conclusions

PYQ 2. Statements: No pen is pencil. All pencils are erasers. Conclusions: I. Some erasers are not pens. II. No eraser is pen. [RRB Group D 2022]

Answer: A) Only I follows

Solution: Pen ∩ Pencil = ∅, Pencil ⊂ Eraser

• Conclusion I: True (pencils are erasers but not pens)
• Conclusion II: Not necessarily (other erasers could be pens)

Exam Tip: Check if conclusion applies to entire set or subset

PYQ 3. Statements: Some doctors are teachers. All teachers are professors. Conclusions: I. Some doctors are professors. II. Some professors are doctors. [RRB ALP 2018]

Answer: C) Both follow

Solution: Doctor ∩ Teacher ≠ ∅, Teacher ⊂ Professor

• Conclusion I: Doctor ∩ Teacher ⊂ Professor (True)
• Conclusion II: Same as I, just reversed (True)

Exam Tip: “Some A are B” = “Some B are A”

PYQ 4. Statements: All books are pages. Some pages are covers. Conclusions: I. Some books are covers. II. Some covers are pages. [RRB JE 2019]

Answer: B) Only II follows

Solution: Book ⊂ Page, Page ∩ Cover ≠ ∅

• Conclusion I: Not necessarily (books could be outside cover intersection)
• Conclusion II: True (some pages are covers means some covers are pages)

Exam Tip: “Some” statements are reversible

PYQ 5. Statements: Some fruits are apples. No apple is vegetable. Conclusions: I. Some fruits are not vegetables. II. No fruit is vegetable. [RPF SI 2019]

Answer: A) Only I follows

Solution: Fruit ∩ Apple ≠ ∅, Apple ∩ Vegetable = ∅

• Conclusion I: True (apple-fruits are not vegetables)
• Conclusion II: Not necessarily (other fruits could be vegetables)

Exam Tip: Don’t overgeneralize from subset to whole set

Speed Tricks & Shortcuts

For Syllogism, provide exam-tested shortcuts:

Common Mistakes to Avoid

Quick Revision Flashcards

Topic Connections

How Syllogism connects to other RRB exam topics:

• Direct Link: Analytical Reasoning - Both test logical deduction skills
• Combined Questions: Often combined with Blood Relations (All mothers are women + Blood relation concepts)
• Foundation For: Data Sufficiency questions build on syllogistic reasoning principles