📑 Topics on this page (Jump to Topic):
📌 1. Four Types of Statements
| Statement | Meaning | Conversion |
|---|---|---|
| All A are B | A wholly inside B | Some B are A |
| Some A are B | A and B overlap | Some B are A |
| No A is B | A and B fully separate | No B is A |
| Some A are not B | Part of A outside B | No definite conversion |
📌 2. Rules for Definite Conclusions
| Statement 1 + Statement 2 | Conclusion |
|---|---|
| All + All | All |
| All + No | No |
| Some + All | Some |
| Some + No | Some not |
| All + Some | No definite |
| Some + Some | No definite |
| No + No | No definite |
💡 Memory Tip: Draw the minimum Venn diagram. A conclusion is definite only if it is true in every possible diagram.
📌 3. Possibility & Either-Or
- 'Some A being B is a possibility' — true unless statements fix 'No A is B'.
- 'All A being B is a possibility' — false if 'Some A are not B' is definite.
- Either-or: two conclusions on the same pair, one 'Some' + one 'No' (or All + Some not), each uncertain alone.
⚠️ Exam Traps:
- 'All A are B' does not give 'All B are A'.
- However odd the statements (All cats are tables), take them as true — don't apply real-world knowledge.
📌 4. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. Statements: All dogs are animals. All animals are living beings. Conclusions: I. All dogs are living beings. II. Some living beings are dogs. Practice
Correct answer: (B)
All + All = All (I); its conversion gives Some (II).
All + All = All (I); its conversion gives Some (II).
Q2. Statements: Some pens are books. All books are notebooks. Conclusions: I. Some pens are notebooks. II. All notebooks are pens. Practice
Correct answer: (C)
Some + All = Some ⇒ I follows; II is not certain.
Some + All = Some ⇒ I follows; II is not certain.
Q3. Statements: All roses are flowers. No flower is a stone. Conclusions: I. No rose is a stone. II. Some stones are roses. Practice
Correct answer: (D)
All + No = No ⇒ I follows, II does not.
All + No = No ⇒ I follows, II does not.
Q4. Statements: All A are B. Some B are C. Conclusions: I. Some A are C. II. No A is C. Practice
Correct answer: (A)
All + Some = no definite; I (Some) and II (No) are complementary on the same pair ⇒ either-or.
All + Some = no definite; I (Some) and II (No) are complementary on the same pair ⇒ either-or.
Q5. Statements: Some teachers are doctors. No doctor is a lawyer. Conclusions: I. Some teachers are not lawyers. II. No teacher is a lawyer. Practice
Correct answer: (B)
Some + No = Some not ⇒ only I.
Some + No = Some not ⇒ only I.
Q6. Statements: All cats are tables. All tables are chairs. Conclusions: I. All chairs are cats. II. Some chairs are tables. Practice
Correct answer: (C)
Conversion of 'All tables are chairs' gives II. I is not certain.
Conversion of 'All tables are chairs' gives II. I is not certain.
Q7. Statements: No apple is an orange. No orange is a mango. Conclusions: I. No apple is a mango. II. Some apples are mangoes. Practice
Correct answer: (D)
No + No = no definite; No and Some are complementary ⇒ either-or.
No + No = no definite; No and Some are complementary ⇒ either-or.
Q8. Statement: All boys are players. Conclusions: I. All players are boys. II. Some players are boys. Practice
Correct answer: (A)
'All' converts to 'Some', not 'All'.
'All' converts to 'Some', not 'All'.
Q9. Statements: Some cars are buses. Some buses are trucks. Conclusions: I. Some cars are trucks. II. Some trucks are buses. Practice
Correct answer: (B)
Some + Some = no definite ⇒ I doesn't follow; II is the conversion of 'Some buses are trucks'.
Some + Some = no definite ⇒ I doesn't follow; II is the conversion of 'Some buses are trucks'.
Q10. Statements: All birds fly. Some fliers are fish. Conclusions: I. Some birds being fish is a possibility. II. All fish fly. Practice
Correct answer: (C)
No negative link between birds and fish ⇒ the possibility holds. II is not certain.
No negative link between birds and fish ⇒ the possibility holds. II is not certain.
Q11. Statements: No book is a pen. All pens are pencils. Conclusions: I. Some pencils are not books. II. No pencil is a book. Practice
Correct answer: (D)
Pencils that are pens are not books ⇒ I follows; other pencils may be books ⇒ II doesn't.
Pencils that are pens are not books ⇒ I follows; other pencils may be books ⇒ II doesn't.
Q12. Statements: All X are Y. All Y are Z. All Z are W. Conclusions: I. All X are W. II. Some W are Y. Practice
Correct answer: (A)
Chain of 'All' ⇒ All X are W; conversion of All Y are W gives II.
Chain of 'All' ⇒ All X are W; conversion of All Y are W gives II.
Q13. Statement: Some fruits are sweet. Conclusions: I. Some fruits are not sweet. II. All fruits being sweet is a possibility. Practice
Correct answer: (B)
'Some' does not give 'Some not' definitely; but 'All' is possible.
'Some' does not give 'Some not' definitely; but 'All' is possible.
Q14. Statement: No A is B. Conclusions: I. No B is A. II. Some A are not B. Practice
Correct answer: (C)
'No' converts to 'No'; and 'No' also implies 'Some not'.
'No' converts to 'No'; and 'No' also implies 'Some not'.
Q15. Statements: All phones are radios. No radio is a TV. Conclusions: I. Some phones are TVs. II. No TV is a phone. Practice
Correct answer: (D)
All + No = No phone is a TV ⇒ its conversion II follows; I doesn't.
All + No = No phone is a TV ⇒ its conversion II follows; I doesn't.
Q16. Statements: Some rivers are lakes. All lakes are seas. Conclusions: I. Some seas are rivers. II. All rivers are seas. Practice
Correct answer: (A)
Some + All = Some rivers are seas; its conversion is I. II is not certain.
Some + All = Some rivers are seas; its conversion is I. II is not certain.
Q17. Statements: All trees are green. Some green are blue. No blue is red. Conclusions: I. Some green are not red. II. No tree is red. Practice
Correct answer: (B)
Some green are blue + No blue is red = Some green are not red (I). Tree-red is not fixed.
Some green are blue + No blue is red = Some green are not red (I). Tree-red is not fixed.
Q18. Statement: All M are N. Conclusions: I. All N being M is a possibility. II. Some N not being M is a possibility. Practice
Correct answer: (C)
M and N may be equal (I possible) or N may be bigger (II possible).
M and N may be equal (I possible) or N may be bigger (II possible).
Q19. Statements: No doctor is a nurse. Some nurses are patients. Conclusions: I. Some patients are not doctors. II. No patient is a doctor. Practice
Correct answer: (D)
Some patients are nurses (conversion) + No nurse is a doctor = Some patients are not doctors.
Some patients are nurses (conversion) + No nurse is a doctor = Some patients are not doctors.
Q20. Statements: All pens are blue. All blue things are heavy. Conclusions: I. Some heavy things are pens. II. All heavy things are blue. Practice
Correct answer: (A)
All pens are heavy ⇒ conversion gives I. II reverses 'All', not certain.
All pens are heavy ⇒ conversion gives I. II reverses 'All', not certain.