Syllogism problems
- 1. Statements:
(a) All peacocks are lions.
(b) Some tigers are peacocks.
Conclusions:
I. Some lions are not tigers.
II. All tigers are lions.
III. Some tigers are lions.
IV. All peacocks are tigers.
Options- A. Only conclusion III follows
- B. Only conclusion IV follows
- C. Only conclusion I follows
- D. Only conclusion II follows Discuss
Correct Answer: Only conclusion III follows
Explanation:
(i) All peacocks are lions ? Universal Affirmative (A-type).
(ii) Some tigers are peacocks ? Particular Affirmative (I-type).
(iii) No tiger is a lion ? Universal Negative (E-type).
(iv) Some tigers are not lions ? Particular Negative (O-type).
Some tigers are peacocks. ? All peacocks are lions.
I + A ? I-type of Conclusion. "Some tigers are lions".
This is Conclusion III.
- 2. Statements:
(a) No mobile is a watch.
(b) All watches are calculators.
Conclusions:
I. No calculator is a mobile.
II. Some calculators are mobiles.
Options- A. Neither Conclusion I nor II follows
- B. Only Conclusion I follows.
- C. Only Conclusion II follows.
- D. Either Conclusion I or II follows. Discuss
Correct Answer: Either Conclusion I or II follows.
Explanation:
No mobile is a watch. ? All watches are calculators.
E + A ? O1 -type of Conclusion. "Some calculators are not mobiles".
Conclusions I and II form Complementary Pair, Therefore, either Conclusion I or Conclusion II follows.
- 3. Statements:
(a) All benches are table.
(b) No table is chair.
Conclusion:
I. All benches are chiars
II. All tables are benches
III. No tables are benches
IV. No benches are chairs
Options- A. Only conclusion II follows
- B. Only conclusion III follows
- C. Only conclusion IV follows
- D. Only conclusion I follows Discuss
Correct Answer: Only conclusion IV follows
Explanation:
First Premise is Universal Affirmative (A-type).
Second Premise is Universal Negative (E-type).
All benches are tables. ? No table is chair
A + E ? E-type of Conclusion "No bench is chair."
This is Conclusion IV.
- 4. Statements:
(a) Some books are mobiles.
(b) Some calculators are mobiles.
Conclusions:
I. Some mobiles are calculators.
II. Some mobiles are books.
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:
Both the Premises are Particular Affirmative (I-type). No Conclusion follows from the two Particular Premises.
Conclusion I is the Converse of the second Premise.
Conclusion II is the converse of the first Premise.
- 5. Statements:
(a) Some stones are gold.
(b) Some gold are banks.
Conclusions:
I. Some banks are stones.
II. Some gold are stones.
III. No stone is bank.
IV. Some banks are gold.
Options- A. Only conclusions II and III follow
- B. Only conclusions II and IV follow
- C. Only conclusions I and IV follow
- D. Only either conclusion III or IV and I follow Discuss
Correct Answer: Only conclusions II and IV follow
Explanation:
Both the Premises are Particular Affirmative (I-type).
No Conclusion follows from the two Particular Premises.
Conclusion II is Converse of the first statement.
Conclusion IV is Converse of the second statement.
Conclusions I and III form Complementary Pair. Therefore, either I or III follows.
- 6. Statements:
(a) All men are bachelors.
(b) Some bachelors are teachers.
(c) Some teachers are spiritual.
Conclusions:
I. All men are spiritual.
II. Some teachers are spiritual.
III. Some men are spiritual.
IV. All teachers are spiritual.
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:
The first Premise is Universal Affirmative (A?type).
The second and the third Premises are Particular Affirmative (I?type).
All men are bachelors. ? Some bachelors are teachers.
A + I ? No Conclusion
Conclusion II is the Converse of the third Premise.
- 7. Statements:
Some food are sweet.
Some food are sour.
Conclusions:
(I) All food are either sweet or sour.
(II) Some sweets are sour.
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 Particular Affirmative (I-type). No Conclusion follows from the two Particular Premises.
- 8. Statements:
Some ladies are beautiful.
Some beautiful. are honest.
All honest are sensitives.
Conclusion 1: Some sensitives are beautiful.
Conclusion 2: Some honest are ladies.
Conclusion 3: Some sensitives are ladies.
Options- A. None of the Conclusion follows.
- B. Only Conclusion 1 follows.
- C. Only Conclusions 1 and 2 follow.
- D. All Conclusions follow. Discuss
Correct Answer: Only Conclusion 1 follows.
Explanation:
The first and second Premises are Particular Affirmative (I-type).
The third Premise is Universal Affirmative (A-type).
Some beautifuls are honest. ? All honest are sensitives.
I + A ? I-type of Conclusion "Some beautifuls are sensitives."
Conclusion 1 is Converse of it.
- 9. Statements:
All pens are pencils.
No pencil is an eraser.
Conclusions:
I. No eraser is a pen.
II. No pen is an eraser.
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: Both conclusions I and II follow
Explanation:
The first Premise is Universal Affirmative (A-type)
The second Premise is Universal Negative (E-type).
All pens are pencils. ? No pencil is an eraser.
A + E ? E-type of Conclusion "No pen is an eraser".
This is Conclusion II.
Conclusion I is the Converse
- 10. Statements:
Some hills are rivers.
Some rivers are deserts.
All deserts are roads.
Conclusions:
I. Some roads are rivers.
II. Some roads are hills.
III. Some deserts are hills.
Options- A. Only conclusion I follows
- B. Only conclusions I and II follow
- C. Only conclusions II and III follow
- D. None follows Discuss
Correct Answer: Only conclusion I follows
Explanation:
First and second Premises are Particular Affirmative (I-type).
Third Premise is Universal Affirmative (A-type).
Some rivers are deserts. All deserts are roads.
I + A ? I-type of Conclusion "Some rivers are roads."
Conclusion I is Converse of it.
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