Syllogism problems
- 1. Statements:
a. Some clerks are poor.
b. A is poor.
Conclusions:
a. A is clerk.
b. A has a large family.
Options- A. Only Conclusion II follows.
- B. Neither Conclusion I nor Conclusion II follows.
- C. Both Conclusions I and II follow
- D. Only Conclusion I follows. Discuss
Correct Answer: Neither Conclusion I nor Conclusion II follows.
Explanation:
Some clerks (not all) are poor and A is poor.
Therefore, it is not certain that A is a clerk. Thus, neither Conclusion I nor Conclusion II follows.
- 2. Statements:
1. All fish are tortoise.
2. No tortoise is a crocodile.
Conclusions:
I. No crocodile is a fish.
II. No fish is a crocodile
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:
First Premise is Universal Affirmative (A-type).
Second Premise is Universal Negative (E-type).
All fish are tortoise. ? No tortoise is a crocodile.
A + E ? E - type of Conclusion "No fish is a crocodile".
This is Conclusion II.
Conclusion I is Converse of it.
- 3. Statements :
No pencil is eraser.
All erasers are sharpeners.
Conclusions:
I. All sharpeners are pencils.
II. All sharpeners are erasers.
Options- A. Only conclusion I follows
- B. Only conclusion II follows
- C. Either conclusion I or conclusion II follows
- D. Neither conclusion I nor conclusion II follows Discuss
Correct Answer: Neither conclusion I nor conclusion II follows
Explanation:
First Premise is Universal Negative (E?type).
Second Premise is Universal Affirmative (A?type).
No pencil is eraser. ? All erasers are sharpeners.
E + A ? O1 ? type of Conclusion. "Some sharpeners are not pencils."
Venn diagrams
Therefore, neither Conclusion I nor Conclusion II follows.
- 4. Statements:
All roses are yellow.
Some roses are flowers.
Conclusions:
I. Some roses are yellow.
II. All roses are flowers.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Neither Conclusion I nor II follows
- D. Both Conclusions I and II follow Discuss
Correct Answer: Only Conclusion I follows
Explanation:
First Premise is Universal Affirmative (A-type).
Some flowers are roses. ? All roses are yellow.
I + A ? I-type of Conclusion "Some flowers are yellow."
Conclusion I is the Implication of the first Premise.
- 5. Statements: All intelligent people are creative.
Conclusion I: Some creative people are intelligent.
Conclusion II: All intelligent people are creative.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Either Conclusion I or II follows
- D. Both Conclusions I and II follow Discuss
Correct Answer: Both Conclusions I and II follow
Explanation:
All intelligent people are creative. It implies that some creative people are intelligent. This is Conclusion I Conclusion II is the same as the statement.
Venn diagram:
- 6. Statements:
1. All cycles are ducks.
2. All ducks are swans.
Conclusions:
I. All swans are cycles.
II. Some swans are cycles.
Options- A. Only Conclusion I follows
- B. Only Conclusion II follows
- C. Both Conclusion I and Conclusion II follow
- D. Neither Conclusion I nor Conclusion II follows Discuss
Correct Answer: Only Conclusion II follows
Explanation:
Both the Premises are Universal Affirmative (A?type).
All cycles are ducks. ? All ducks are swans.
A + A ? A?type of Conclusion "All cycles are swans."
Conclusion II is the Converse of it.
- 7. Statements:
Some books are novels.
All novels are magazines. Some magazines are journals.
Conclusions:
I. Some novels are journals.
II. Some books are magazines.
III. All books are magazines.
IV. No novel is a journal.
Options- A. Only conclusion II follows
- B. Only conclusion III follows
- C. Either conclusion I or II follows
- D. Either conclusion I or IV and conclusion II follow Discuss
Correct Answer: Either conclusion I or IV and conclusion II follow
Explanation:
First and third Premises are Particular Affirmative (I-type).
Second Premise is Universal Affirmative (A-type).
Some books are novels. ? All novels are magazines.
I + A ? I-type of Conclusion. "Some books are magazines."
It is Conclusion II.
Conclusions I and IV form Complementary Pair. Therefore, either Conclusion I or IV follows.
- 8. Statements:
(a) Blue is Black and some Black is red.
(b) All red is Green but not Yellow
Conclusions:
I. Some Blue is Green.
II. No Black is Yellow.
III. Some Black is not Yellow.
IV. No Black is Green.
Options- A. Only I and II follow
- B. Only II and IV follow
- C. Only I and III follow
- D. Only I, II and IV follow Discuss
Correct Answer: Only I and II follow
Explanation:
Some blue is red and All red is green. Therefore, some blue is green.
Clearly, no black is yellow. Thus, only Conclusions I and II follow.
- 9. Statements:
(a) Some buses are four wheelers.
(b) All four wheelers are vans.
Conclusions:
I. Some vans are buses.
II. Some buses are vans.
Options- A. Either conclusion I or II follows
- B. Both conclusions I and II follow
- C. Only conclusion I follows s
- D. Only conclusion II follows Discuss
Correct Answer: Both conclusions I and II follow
Explanation:
Some buses are four-wheelers. ? All four-wheelers are vans.
I + A ? I-type of Conclusion. "Some buses are vans".
This is Conclusion II.
Conclusion I is Converse of this Conclusion.
- 10. Statements:
(a) All teachers are experienced.
(b) Some teachers are spinsters.
Conclusions:
I. Some experienced are spinsters.
II. Some spinsters are experienced.
Options- A. Only conclusion II follows
- B. Either conclusion I or II follows
- C. Both conclusion I and II follow
- D. Only conclusion I follows Discuss
Correct Answer: Both conclusion I and II follow
Explanation:
First Premise is Universal Affirmative (A-type).
Second Premise is Particular Affirmative (I-type).
Some spinsters are teachers. ? All teachers are experienced.
I + A ? I-type of Conclusion "Some spinsters are experienced."
This is Conclusion II.
Conclusion I is Converse of it.
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