Syllogism problems
- 1. Statements :
Some peons are poor.
X is poor.
Conclusions :
I. X is a peon.
II. X has a large family.
Options- A. Only I follows
- B. Only II follows
- C. Both I & II follow
- D. Neither I nor II follows Discuss
Correct Answer: Neither I nor II follows
Explanation:
The first premise is particular Affirmative (I- Type). The second premise is Universal Affirmative (A-Type).
We can align the premises by converting the first premise and changing their order. Thus,
X is poor ? Some poors are peons have a doctorate degree.
We know that,
A + I = No conclusion.
- 2. Statements:
(A) All basketball players are tall men.
(B). All basketball players are athletes.
Conclusions:
I. All tall men are basketball players.
II. All athletes are basketball players.
Options- A. I alone can be drawn
- B. Both can be drawn
- C. Both cannot be drawn
- D. II alone can be drawn Discuss
Correct Answer: Both cannot be drawn
Explanation:
Both the Premises are Universal Affirmative (A-type). We can align the Premises by taking converse of any of the premises.
Some tall men are basketball players ? All basketball players are athletes.
I + A ?I - type of conclusion "Some tall men are athletes".
- 3. Statements:
Some doctors are teachers.
All teachers are counsellors.
Conclusions:
I. Some counsellors are not teachers.
II. Some doctors are counsellors
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Both conclusion I and II follow
- D. Neither conclusion I nor II follow Discuss
Correct Answer: Only conclusion II follows
Explanation:
First premise is Particular Affirmative (I?type).
Second premise is Universal Affirmative (I-type).
Both the premises are already aligned. Thus,
Some doctors are teachers ? All teachers are counsellors.
We know that, I + A ? I-type conclusion.
Therefor, our derived conclusion would be:
"Some doctors are counsellors". Thus, only conclusion II follows.
- 4. Statement:
(a) All politicians are intelligent
(b) Some women are politicians
Conclusions:
I. Some women are intelligent
II. All those intelligent are women.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Both conclusions I & II follow
- D. Neither conclusion I nor conclusion II follows Discuss
Correct Answer: Only conclusion I follows
Explanation:
Some women are politicians. ? All politicians are intelligents.
We know that,
I + A ?I?type Conclusion Thus, our derived Conclusion would be: "Some women are intelligent".
- 5. Statements:
(A) Some cats are dogs.
(B) Some dogs are stones.
Conclusions:
I. No cat is stone.
II. All dogs are stones.
III. Some stones are cats.
IV. No dog is cat.
Options- A. Only I and III follow
- B. Only II and III follow
- C. Only I, III and IV follow
- D. None follows Discuss
Correct Answer: None follows
Explanation:
Both the Premises are Particular Affirmative (I-type).
No Conclusion follows from the two Particular Premises.
Conclusions I and III form Complementary Pair. Therefore, either Conclusion I or III follows. Considering the given Options we can select option (4) as the answer.
- 6. Statements:
A. All girls are proud.
B. All proud will be humiliated one day.
Inferences:
I. All girls will be humiliated one day.
II. Some girls will be humiliated one day.
Options- A. Only I follows
- B. Only II follows
- C. Both I & II follow
- D. Neither of them follows Discuss
Correct Answer: Both I & II follow
Explanation:
Both the Premises are Universal Affirmative (A-type).
Both the Premises are already aligned.
All girls are proud ? All proud will be humiliated one day
We know that,
A + A ? A ? type Conclusion Therefore, our derived Conclusion would be:
"All girls will be humiliated one day".
Conclusion II is the converse of the derived Conclusion. Thus, both the Conclusions follow.
- 7. Statements:
P. All men are women.
Q. All women are crazy.
Conclusions:
I. All men are crazy.
II. All the crazy are men.
III. Some of the crazy are men.
IV. Some of the crazy are women.
Options- A. None of the conclusions follows
- B. All the conclusions follow
- C. Only I, III and IV follow
- D. Only II and III follow Discuss
Correct Answer: Only I, III and IV follow
Explanation:
Both the Premises are Universal Affirmative (A-type).
All men are women. ? All women are crazy.
A + A ? A ? type of Conclusion
"All men are crazy".
This is Conclusion I. Conclusion III is the Converse of it.
Conclusion IV is the Converse of Statement Q.
- 8. 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:
We can align the premises by converting the second premise.
All Americans are English speaking. ? No English speakers are Eskimos.
We know that,
A + E ? E type conclusion Thus, our derived conclusion would be:
"No Americans are Eskimos."
Conclusion I is the converse of the derived conclusion.
Conclusion II is the converse of second premise.
- 9. Statements:
(a) All frogs are tortoises.
(b) No tortoise is a crocodile.
Conclusions:
I. No crocodile is a frog.
II. No frog is a crocodile.
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:
First Premise is Universal Affirmative (A-type).
Second Premise is Universal Negative (E-type).
All frogs are tortoises. ? No tortoise is a crocodile.
A + E ? E-type of Conclusion "No frog is a crocodile".
This is Conclusion II.
Conclusion I is Converse of this Conclusion.
- 10. Statements:
(a) All dogs are books
(b) All books are pictures.
Conclusion:
I. All dogs are pictures.
II. All books are dogs.
III. All pictures are dogs.
IV. Some pictures are books.
Options- A. Only I and IV follow
- B. Only II and III follow
- C. Either II or III follows
- D. Either II or IV follows Discuss
Correct Answer: Only I and IV follow
Explanation:
Both the Premises are Universal Affirmative (A-type).
All dogs are books. ? All books are pictures.
A + A ? A-type of Conclusion "All dogs are pictures."
This is Conclusion I.
Conclusion IV is Converse of the second Premise.
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