Syllogism problems
- 1. Statements:
(a) All children are students.
(b) All students are players.
Conclusions:
I. All cricketers are students.
II. All children are players.
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: Only conclusion II follows.
Explanation:
Both the Premises are Universal Affirmative (A?type).
All children are students. ? All students are players.
A + A ? A?type of Conclusion
All children are players.¸
This is Conclusion II.
- 2. Statements:
a. All metals are silver.
b. All silver are diamond.
c. Some diamonds are gold.
d. Some gold are marbles.
Conclusions:
I. Some gold are metals.
II. All metals are diamond.
III. Some silver are marble.
IV. Some gold are silver.
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 II follows.
Explanation:
All metals are silver. ? All silver are diamond.
A + A ? A ? type of Conclusion "All metals are diamond".
This is Conclusion II.
- 3. Statements:
I. Some cats are dogs.
II. No dog is a toy.
Conclusions:
I. Some dogs are cats.
II. Some toys are cats.
III. Some cats are not toys.
IV: All toys are cats.
Options- A. Only Conclusions I and III follow
- B. Only Conclusions II and III follow
- C. Only Conclusions I and II follow
- D. Only Conclusion I follows Discuss
Correct Answer: Only Conclusions I and III follow
Explanation:
First Premise is Particular Affirmative (I-type).
Second Premise is Universal Negative (E-type).
Some cats are dogs. ? No dog is a toy.
I + E ? O ? type of Conclusion "Some cats are not toys."
This is Conclusion III. Conclusion I is Converse of the first Premise.
- 4. Statements:
Some scales are pencils.
Some erasers are pencils.
Conclusions:
I. Some pencils are erasers.
II. Some pencils are scales.
Options- A. Only I follows
- B. Only II follows
- C. Both I and II follow
- D. Neither I nor II follows Discuss
Correct Answer: Both I and II follow
Explanation:
Both the Premises are Particular Affirmative (I-type).
No Conclusion follows from the two Particular Premises.
Conclusion I is Converse of the second Premise.
Conclusion II is Converse of the first Premise.
- 5. Statements
All cows are animals.
All deers are cows.
Conclusions
I. All deers are animals.
II. All animals are cows.
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: Only conclusion I follows.
Explanation:
Both the Premises are Universal Affirmative (A-type).
All deers are cows. ? All cows are animals.
A + A ? A-type of Conclusion "All deers are animals"
This is Conclusion I.
- 6. Statements:
All chickens are birds.
Some chickens are hens.
Female birds lay eggs.
Conclusions:
I. All birds lay eggs.
II. Some hens are birds.
III. Some chickens are not hens.
Options- A. Conclusions II and III both follow
- B. All conclusions I, II and III follow
- C. Only conclusion I follows
- D. Only conclusion II follows Discuss
Correct Answer: Only conclusion II follows
Explanation:
First Premise is Universal Affirmative (A-type).
Second Premise is Particular Affirmative (I-type).
Some hens are chickens. ? All chickens are birds.
I + A ? I ? type of Conclusion "Some hens are birds."
This is Conclusion II.
- 7. Statements:
All Americans are English ? speaking.
No Eskimos are English ? speaking
Conclusions:
I. No Eskimos are Americans.
II. No English ? speakers are Eskimos.
Options- A. Only I follows.
- B. Neither I nor II follows.
- C. Only II follows.
- D. Both I and II follow. Discuss
Correct Answer: Both I and II follow.
Explanation:
First Premise is Universal Affirmative (A-type).
Second Premise is Universal Negative (E-type).
All Americans are English-speaking. ? No English-speaking are Eskimos.
A + E ? E-type of Conclusion "No American is Eskimo."
Conclusion I is Converse of it.
Conclusion II is Converse of the second Premise.
- 8. Statement:
Cactus plants are fleshy but need least water.
Conclusions:
I. All fleshy plants are cactus.
II. Cactus plants need least water.
Options- A. Neither I nor II follows
- B. Only II follows
- C. Both I and II follows
- D. Only I follows Discuss
Correct Answer: Only II follows
Explanation:
Cactus plants are fleshy.
And, Cactus plants need least water.
Therefore, only Conclusion II follows.
The Converse of Universal Affirmative Premises is Particular Affirmative Premise.
- 9. Statements:
I. All poets are day dreamers.
II. All painters are day dreamers.
Conclusions:
I. All painters are poets.
II. Some day dreamers are not painters
Options- A. Both I and II follow
- B. Neither I nor II follows
- C. Only I follows
- D. Only II follows Discuss
Correct Answer: Neither I nor II follows
Explanation:
Both the Premises are Universal Affirmative (A?type).
But, these two Premises are not aligned properly.
All poets are day dreamers. ? Some day dreamers are painters.
A + I ? No Conclusion
- 10. Statements
a. All children are students.
b. All students are players.
Conclusions
/I. All cricketers are students.
II. All children are players.
Options- A. Only conclusion I follows.
- B. Neither conclusion I nor II follows.
- C. Both conclusions I and II follow.
- D. Only conclusion II follows. Discuss
Correct Answer: Only conclusion II follows.
Explanation:
Both the Premises are Universal Affirmative (A-type).
All children are students. ? All students are players.
A + A ? A - type of Conclusion "All children are players".
This is Conclusion II.
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