Syllogism problems
- 1. Statements:
(a) All clerks are typists.
(b) Some typists are stenos.
Conclusions:
I. Some stenos are clerks.
II. No steno is a clerk.
III. All typists are clerks.
IV. All clerks are stenos.
Options- A. All the conclusions follow
- B. None of conclusions follow
- C. Either I or II follows
- D. Only IV follows Discuss
Correct Answer: Either I or II follows
Explanation:
First Premise is Universal Affirmative (A-type).
Second Premise is Particular Affirmative (I-type).
All clerks are typists. ? Some typists are stenos.
A + I ?No Conclusion
Conclusions I and II form Complementary Pair. Therefore, either I or II follows.
- 2. Statements:
(a) All players are educated.
(b) All educated are cultured.
Inferences:
I. All players are cultured.
II. All cultured persons are players.
Options- A. Only inference I follows
- B. Only inference II follows
- C. Both inference I and II follows
- D. Neither inference I nor II follows Discuss
Correct Answer: Only inference I follows
Explanation:
Both the Premises are Universal Affirmative (A - type).
All players are educated. ? All educated are cultured.
A + A ? A?type of Conclusion "All players are cultured."
This is Conclusion I.
- 3. Statements:
Some books are Magazines.
Some Magazines are Novels.
Conclusions:
(I) Some books are Novels.
(II) Some Novels are Magazines.
Options- A. Only (I) follows
- B. Only (II) follows
- C. Either (I) or (II) follows
- D. Neither (I) nor (II) follows Discuss
Correct Answer: Only (II) follows
Explanation:
Both the Premises are Particular Affirmative (I-type).
No Conclusion follows from the two Particular Premises.
Conclusion II is Converse of the second Premise.
- 4. Statements :
All animals are birds.
Some animals are human beings.
Conclusions :
I. Some human beings are birds.
II. Some birds are human beings.
Options- A. I follows
- B. II follows
- C. Both I or II follow
- D. Neither I nor II follows Discuss
Correct Answer: Both I or II follow
Explanation:
First Premise is Universal Affirmative (A - type).
Second Premise is Particular Affirmative (I - type).
Some human beings are animals. ? All animals are birds.
I + A ? I-type of Conclusion "Some human beings are birds".
This is Conclusion I.
Conclusion II is converse of it.
- 5. Statements:
All women are cats.
All cats are rats.
Conclusions:
I. All women are rats.
II. All rats are women.
Options- A. Neither conclusion I nor II follows
- B. Only conclusion I follows
- C. Only conclusion II follows
- D. Both conclusions I and II follow Discuss
Correct Answer: Only conclusion I follows
Explanation:
Both the premises are Universal Affirmative (A-type).
All women are cats. ? All cats are rats.
A + A ? A-type of Conclusion "All women are rats."
This is Conclusion I.
- 6. Statements:
(1) All books are trees.
(2) All trees are lions.
Conclusions:
I. All books are lions.
II. All lions are books.
III. All trees are books.
IV. Some lions are books.
Options- A. Only II and III follow.
- B. Only I and IV follow.
- C. None of the conclusions follows.
- D. All conclusions follow. Discuss
Correct Answer: Only I and IV follow.
Explanation:
Both the Premises are Universal Affirmative (A-type).
All books are trees. ? All trees are lions.
A + A ? A-type of Conclusion. ''All books are lions''.
This is Conclusion I.
Conclusion IV is converse of it.
- 7. Statements:
A. All clerks are superintendents.
B. All superintendents are managers.
C. All managers are supervisors.
Conclusions:
I. All supervisors are clerks.
II. Some clerks are supervisors.
III. Some managers are clerks.
IV. All superintendents are clerks.
Options- A. Only conclusion I
- B. Only conclusion II
- C. Only conclusion III
- D. Only conclusion IV Discuss
Correct Answer:
Explanation:
All the three Premises are Universal Affirmative (A - type)
All clerks are superintendents. ? All superintendents are managers.
A + A ? A ? type of Conclusion ''All clerks are managers.''
Conclusion III is Converse of it.
All clerks are managers. ? All managers are supervisors.
A + A ? A ? type of Conclusion ''All clerk are supervisors.''
Conclusions II is its Implication.
All superintendents are managers. ? All managers are supervisors.
A + A ? A ? type of Conclusion ''All superintendents are supervisors.''
Conclusions II and III follow
- 8. Statements:
(a) Some schools are Laboratories.
(b) All Laboratories are theatres.
Conclusions:
I. Some theatres are schools.
II. No school is a theatre.
Options- A. Conclusion II follows
- B. Both Conclusions I and II follow
- C. Neither Conclusion I nor II follows
- D. Conclusion I follows Discuss
Correct Answer: Conclusion I follows
Explanation:
First Premise is Particular Affirmative (I-type)
Second Premise is Universal Affirmative (A-type).
Some schools are laboratories. ? All laboratories are theatres.
I + A ? I?type of Conclusion "Some schools are theatres".
Conclusion I is Converse of it.
- 9. Statements:
Some boys are men.
No man is black.
Conclusions:
I. Some boys are not black.
II. Some men are boys.
Options- A. Only Conclusion I follows.
- B. Only Conclusion II follows.
- C. Either I or II follows.
- D. Neither I nor II follows. Discuss
Correct Answer:
Explanation:
First Premise is Particular Affirmative (I?type).
Second Premise is Universal Negative (E?type).
Some boys are men. ? No men is black.
I + E ? O ? type of Conclusion "Some boys are not black."
This is Conclusion I.
Conclusion II is the Converse of the first Premise.
Thus, both the Conclusions follow.
- 10. Statements
(a) No teacher comes to the school on a bicycle.
(b) Anand comes to the school on a bicycle.
Conclusions
I. Anand is not a teacher
II. Anand is a student.
Options- A. Conclusion II alone can be drawn.
- B. Both conclusions cannot be drawn.
- C. Both conclusions can be drawn.
- D. Conclusion I alone can be drawn. Discuss
Correct Answer: Conclusion I alone can be drawn.
Explanation:
No teacher comes to the school on a bicycle. Therefore, Anand cannot be a teacher. Anand is either student or clerical staff. Therefore, only Conclusion I follows.
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