Syllogism problems
- 1. Statements:
(a) All books are boxes.
(b) All boxes are pens.
(c) All pens are papers.
Conclusions:
I. Some papers are books.
II. All books are papers.
III. Some pens are books.
IV. All boxes are books.
Options- A. Only conclusions I and III follow
- B. Either conclusion II or IV follows
- C. Only conclusions I, II and III follow
- D. Either conclusion I or II or III follows Discuss
Correct Answer: Only conclusions I, II and III follow
Explanation:
All the three statements are Universal Affirmative (A-type).
All books are boxes. ? All boxes are pens.
A + A ? A-type of Conclusion "All books are pens."
Conclusion III is Converse of it.
All books are pens. ?All pens are papers.
A + A ? A-type of Conclusion "All books are papers."
This is Conclusion II.
Conclusion I is Converse of it.
All boxes are pens. ? All pens are papers.
A + A ? A-type of Conclusion "All boxes are papers."
- 2. Statements:
Some teachers are students.
All students are girls.
Conclusions:
(I) All teachers are girls.
(II) Some girls are teachers.
(III) Some girls are students.
(IV) All students are teachers.
Options- A. Only (I) follows
- B. Only (I), (II), and (III) follow
- C. Only (II) and (III) follow
- D. All follow Discuss
Correct Answer: Only (II) and (III) follow
Explanation:
First Premise is Particular Affirmative (I-type).
Second Premise is Universal Affirmative (A-type).
Some teachers are students. ? All students are girls.
I + A ? I-type of Conclusion "Some teachers are girls".
Conclusion II is Converse of it.
Conclusion III is Converse of the second Premise.
- 3. Statement:
(a) All students like excursions.
(b) Some students like laboratory experiments.
Conclusions:
(I) Students who like laboratory experiments also like excursions.
(II) Some students do not like laboratory experiments but like excursions.
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: Both Conclusions I and II follow
Explanation:
The given statements can be illustrated as:
- 4. Statements:
All hens are cocks.
No cock is black.
Conclusions:
I. All cocks are hens.
II. No hen is black.
Options- A. Only conclusion I is valid
- B. Only conclusion II is valid
- C. Both the conclusions are valid
- D. Both the conclusions are invalid Discuss
Correct Answer: Only conclusion II is valid
Explanation:
All hens are cocks. (A) ? No cock is black. (E)
A + E ? E- type of conclusion "No hen is black."
This is Conclusion II.
- 5. Statements:
Dogs have four legs.
Tables have four legs.
Conclusions
I. Tables are dogs.
II. Dogs are tables.
Options- A. Only I follows
- B. Only II follows
- C. Either I or II follows
- D. Neither I nor II follows Discuss
Correct Answer: Neither I nor II follows
Explanation:
The given statement can be shown by the following diagram :
- 6. Statements:
(a) All English movies are violent.
(b) Some people like watching English movies.
Conclusions:
I. All people watching English movies like violence.
II. All people who like violence watch English movies.
Options- A. Only I follows
- B. Only II follows
- C. Neither I nor II follows
- D. Both I and II follow Discuss
Correct Answer: Only I follows
Explanation:
Only Conclusion I follows. As all English movies are violent, the people who like watching English movies like violence. But it is not necessary that all people who like violence watch English movies.
- 7. Statements:
(a) All cupboards are watches.
(b) All watches are costly.
Inferences:
I. All cupboards are costly.
II. Some costly things are cupboards.
Options- A. Only inference I follows
- B. Only inference II follows
- C. Both of them follow
- D. Neither of them follows Discuss
Correct Answer: Both of them follow
Explanation:
Both the Premises are Universal Affirmative (A-type).
All cupboards are watches. ? All watches are costly.
A + A ? A-type of Conclusion "All cupboards are costly."
This is Conclusion I.
Conclusion II is converse of it.
- 8. Statements:
All fruits are sweet.
All sweet things are not good for health.
Conclusions:
(I) All fruits are not good for health.
(II) Some fruits are not good for health.
Options- A. Only (I) follows
- B. Only (II) follows
- C. Neither (I) nor (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 can be written in the form of Universal Negative (E-type) as
No sweet thing is good for health
All fruits are sweet. ? No sweet thing is good for health.
A + E ? E?type of Conclusion "No fruit is good for health".
Thus both the Conclusions follow.
- 9. Statements:
(a) All pens are papers.
(b) No eraser is a paper.
Conclusions:
I. No eraser is a pen.
II. Some papers are pens.
Options- A. Both Conclusions I and II follow.
- B. Only Conclusion I follows.
- C. Only Conclusion II follows.
- D. Neither Conclusion I nor II follows. Discuss
Correct Answer: Both Conclusions I and II follow.
Explanation:
(i) All pens are papers ? Universal Affirmative (A-type).
(ii) Some houses are lakes ? Particular Affirmative (I-type).
(iii) No eraser is paper ? Universal Negative (E-type).
(iv) Some erasers are not papers ? Particular Negative (O-type).
All pens are papers. ? No paper is an eraser.
A + E ? E-type of Conclusion. "No pen is an eraser".
Conclusion I is Converse of it.
Conclusion II is Converse of the first Premise.
- 10. Statements:
(a) No girl is a parrot.
(b) Sowmya is a girl.
Conclusions:
I. Sowmya is not a parrot.
II. All girls are not Sowmya.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either conclusion I or II follows
- D. Neither conclusion I nor II follows Discuss
Correct Answer: Only conclusion I follows
Explanation:
First Premise is Universal Negative (E-type).
Second Premise is Universal Affirmative (A-type).
Sowmya is a girl.? No girl is a parrot.
A + E ? E-type of Conclusion. "Sowmya is not a parrot."
This is Conclusion I.
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