Syllogism problems
- 1. Statement:
Some tablets are capsules.
All capsules are syrups.
Some syrups are medicines
Conclusions:
I. Some syrups are powders.
II. Some syrups are tablets.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer:
Explanation:
Some syrups are medicines + All medicine are powder = I + A + I = Some syrups are powders.
Hence I follow. Some tablets are capsules + All capsules are syrups = I + A + I = Some tablets are syrups ? conversion ? Some syrups are tablets (I). Hence II follows.
- 2. Statement:
All benches are cots.
No cot is lamp.
Some lamps are candles.
Conclusions:
I. Some cots are benches.
II. Some candles are cost.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer: if conclusion I follow
Explanation:
All benches are cots (A) ? conversion ? Some cots are benches (I) Hence follows. No cot is lamp + Some lamps are candles = I + E = O* = Some candles are not cots Hence II does not follow.
- 3. Statement:
Some cats are dogs.
All dogs are goats.
All goats are walls.
Conclusions:
I. Some walls are dogs.
II. Some walls are cats.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer:
Explanation:
All dogs are goats + All goats are walls = A + A = A = All dogs are walls. (I) Hence I follows. Some cats are dogs + All dogs are walls = 1 + A = I = Some cats are wall ? conversion ? Some walls are cats. (I) Hence II follows.
- 4. Statement:
Some buildings are benches.
Some sofas are benches.
Some benches are sofas.
Conclusions:
I. Some tables are sofas.
II. No table is sofa.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer: if either conclusion I or II follows
Explanation:
Some sofas are benches + Some benches are tables = I + I = No conclusion. Hence I and II do not follow by combination. However, since they make a complementary E-I pair, either of the two must follow.
- 5. Statement:
All rats are bats.
Some bats are desks.
All desks are chairs.
Conclusions:
I. Some desks are rats.
II. Some chair are rats.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer: if neither conclusion I nor II follows
Explanation:
All rats are bats + Some bats are desks = I + A = No conclusion Hence I and subsequently II do not follow.
- 6. Statement:
Some roads are ponds.
All ponds are stores.
Some stores are bags.
Conclusions:
I. Some bags are ponds.
II. Some stores are roads.
Options- A. if conclusion I follow
- B. if conclusion II follows
- C. if either conclusion I or II follows
- D. if neither conclusion I nor II follows Discuss
Correct Answer: if conclusion II follows
Explanation:
All ponds are stores + Some stores are bags = I + A = No conclusion Hence I does not follow. Some roads are ponds + All ponds are stores = I + A = I = Some roads are stores ? conversion ? Some stores are roads (I) Hence II follows.
- 7. Two statements are followed by alternatives. Mark the correct alternative that follows :
All Asians are wise.
All Chinese are Asian Therefore,
Options- A. Some Chinese are wise
- B. All wise are Chinese
- C. All Chinese are wise
- D. No conclusion follows Discuss
Correct Answer: All Chinese are wise
Explanation:
Since both the Premises are Universal Affirmative (A - type) and these can be aligned by changing the order of Premises, the Conclusion should be Universal Affirmative.
All Chinese are Asians. ? All Asians are wise.
Therefore, All Chinese are wise. This is conclusion (3).
Here, it should be noted that the Conclusion given in option (1) is the implication of the derived Conclusion and hence it is also valid.
- 8. Statements:
(a) All books are novels.
(b) Some novels are poems.
Conclusions:
(I) Some books are poems.
(II) Some poems are novels.
Options- A. Only conclusion (II) follows
- B. Neither conclusion (I) nor (II) follows
- C. Both conclusions (I) and (II) follow
- D. Only conclusion (I) follows Discuss
Correct Answer: Only conclusion (II) follows
Explanation:
First Premise in Universal Affirmative (A - type).
Second Premise is Particular Affirmative (I - type).
All books are novels. ? Some novels are poems.
A + I ? No Conclusion
Conclusion II is Converse of the second Premise.
- 9. Statements:
I. Some birds are clouds.
II. Horse is a bird.
Conclusions:
I. Some clouds are birds.
II. Horse is not a cloud.
Options- A. Conclusion I follows.
- B. Conclusion II follows.
- C. Either conclusion I or II follows.
- D. Neither conclusion I nor II follows. Discuss
Correct Answer: Conclusion I follows.
Explanation:
Statement I is Particular Affirmative (I-type)
Statement II is Universal Affirmative (A-type).
Horse is a bird. ? Some birds are clouds.
A + I ? No Conclusion
Conclusion I is Converse of the Statement I.
- 10. Statements:
(a) Some politicians are social workers.
(b) All doctors are social workers.
Conclusions:
I. Some doctors are politicians
II. Some social workers are doctors as well as politicians
Options- A. Neither Conclusion I nor II follows.
- B. Only Conclusion II follows.
- C. Both Conclusions I and II follow.
- D. Only Conclusion I follows. Discuss
Correct Answer: Neither Conclusion I nor II follows.
Explanation:
First Premise is Particular Affirmative (I ? type).
Second Premise is Universal Affirmative (A ? type).
All doctors are social workers. ? Some social workers are politicians.
A + I ? No Conclusion.
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