Syllogism problems
- 1. Statements:
(a) No flower is a pot.
(b) No pot is a garden.
Conclusions:
I. No flower is a garden.
II. All gardens are pots.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Both conclusions I and II follow
- D. Neither conclusion I nor II follows Discuss
Correct Answer: Neither conclusion I nor II follows
Explanation:
Both the Premises are Universal Negative (E - type).
No Conclusion follows from the two negative Premises.
- 2. Statements:
(a) Most players are men.
(b) Some men are singers.
Conclusions:
I. Some singers are men.
II. Some players are singers.
Options- A. Only conclusion I follows
- B. Only conclusion II follows.
- C. Neither conclusion I or II follows
- D. Both conclusions I and II follow Discuss
Correct Answer: Only conclusion I follows
Explanation:
The first Premise is Universal Affirmative (A-type).
The second Premise is Particular Affirmative (I-type).
Most players are men. ? Some man are singers.
A + I ? No Conclusion
Conclusion I is Converse of the second statement.
- 3. Statements:
(a) All buses are houses.
(b) Some houses are lakes.
Conclusions:
I. Some buses are lakes.
II. Some lakes are buses.
III. Some lakes are houses.
IV. Some houses are buses.
Options- A. All Conclusions follow.
- B. Only Conclusions II and III follow.
- C. Only Conclusions I and II follow.
- D. Only Conclusions III and IV follow. Discuss
Correct Answer: Only Conclusions III and IV follow.
Explanation:
All buses are houses. ? Some houses are lakes.
A + I ? No Conclusion
Conclusion III is Converse of the second Premise.
Conclusion IV is Converse of the first Premise.
- 4. Statements:
All students are boys.
No boy is dull.
Conclusions:
I. There are no girls in the class.
II. No student is dull.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Both conclusions I and II follow
- D. Neither conclusion I nor conclusion II follows Discuss
Correct Answer: Only conclusion II follows
Explanation:
First Premise is Universal Affirmative and the second Premise is Universal Negative (E-type).
All students are boys. ? No boy is dull.
A + E ? E?type of Conclusion "No student is dull"
This is conclusion II.
- 5. Statements:
a. All apples are bananas.
b. All bananas are sweet.
Conclusions:
I. Some apples are sweet.
II. Some bananas are apples.
Options- A. Conclusion I follows.
- B. Conclusion II follows.
- C. Either conclusion I or II follows.
- D. Both conclusions I and II follow. Discuss
Correct Answer: Both conclusions I and II follow.
Explanation:
(i) All apples are bananas ? Universal Affirmative (A-type).
(ii) Some apples are sweet ? Particular Affirmative (I-type).
(iii) No apple is banana ? Universal Negative (E-type)
(iv) Some apples are not bananas ? Particular Negative (O-type)
All apples are bananas. ? All bananas are sweet.
A + A ? A ? type of Conclusion "All apples are sweet."
Conclusion I is the Implication of it.
Conclusion II is Converse of the first Premise.
- 6. Statements:
a. Some years are decades.
b. All centuries are decades.
Conclusions:
I. Some centuries are years.
II. Some decades are years.
III. No century is a year.
Options- A. Only conclusion II follows
- B. Only conclusions I and II follow
- C. Only conclusions I and III follow
- D. Only conclusion I follows Discuss
Correct Answer:
Explanation:
First Premise is Particular Affirmative (I-type).
Second Premise is Universal Affirmative (A-type).
All centuries are decades. ? Some decades are years.
A + I ? No Conclusion
Conclusion II is Converse of the first Premise.
Conclusions I and III form Complementary Pair. Therefore, either I or III follows.
- 7. Statement
I: Ankit is a singer.
II: All the singers are fat.
Conclusions:
I. Ankit is fat.
II. All fat men are singers.
III. Fat men are not singers.
IV. Ankit is not fat.
Options- A. Only Conclusion I follows.
- B. Only Conclusion II follows.
- C. Only Conclusion III follows.
- D. Only Conclusion IV follows. Discuss
Correct Answer: Only Conclusion I follows.
Explanation:
All the singers are fat and Ankit is a singer. So, Ankit is fat.
- 8. Statements:
1. All animals are four footed.
2. Dog has two legs.
Conclusions:
I. Dog is not an animal.
II. Dog is an animal.
Options- A. If only I follows
- B. If only II follows
- C. If neither I nor II follows
- D. If both I and II follow Discuss
Correct Answer: If only I follows
Explanation:
All animals (without exception) are four?footed.
Dog has two legs. Therefore dog is not an animal.
Thus, only Conclusion I follows.
- 9. Statements:
1. All mangoes are golden in colour.
2. No golden coloured things are cheap.
Conclusions:
I. All mangoes are cheap.
II. Golden?coloured mangoes are not cheap.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Either Conclusion I or Conclusion II follows
- D. Both Conclusions I and II follow Discuss
Correct Answer: Only Conclusion II follows
Explanation:
First Premise is Universal Affirmative (A?type).
Second Premise is Universal Negative (E?type).
All mangoes are golden in colour. It implies that all mangoes without an exception are golden in colour.
No golden coloured things are cheap.
Thus, Conclusion II follows.
- 10. Statements:
Some flies are ants.
All insects are ants.
Conclusions:
I. All flies are ants.
II. Some ants are insects.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Both Conclusion I and Conclusion II follow
- D. Neither Conclusion I nor Conclusion II follows Discuss
Correct Answer: Only Conclusion II follows
Explanation:
First Premise is Particular Affirmative (I?type).
Second Premise is Universal Affirmative (A?type).
All insects are ants. ? Some ants are flies.
A + I ? No Conclusion
Conclusion II is the Converse of the second Premise.
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