Read the given statements and conclusions carefully. Assuming that the information given in the statements is true, even if it appears to be at variance with commonly known facts, decide which of the given conclusions logically follow(s) from the statements.
Statements:
No city is a country.
All towns are cities.
Conclusions:
I. No town is a country.
II. Some towns are countries.
- AEither conclusion I or II follows
- BOnly conclusion I follows
- COnly conclusion II follows
- DBoth conclusions I and II follow
Solution & Step-by-step Explanation
Let's translate the statements into set relationships:
"All towns are cities" → The circle for Towns is entirely enclosed inside the circle for Cities.
"No city is a country" → The circle for Cities and the circle for Countries have zero overlap.
Now, evaluating the conclusions:
Conclusion I: "No town is a country." Since all towns are inside cities, and no city can enter the country boundary, towns can never intersect with countries. Hence, this conclusion is true.
Conclusion II: "Some towns are countries." This is completely impossible based on our diagram. Hence, this conclusion is false.
Thus, only conclusion I follows.
"All towns are cities" → The circle for Towns is entirely enclosed inside the circle for Cities.
"No city is a country" → The circle for Cities and the circle for Countries have zero overlap.
Now, evaluating the conclusions:
Conclusion I: "No town is a country." Since all towns are inside cities, and no city can enter the country boundary, towns can never intersect with countries. Hence, this conclusion is true.
Conclusion II: "Some towns are countries." This is completely impossible based on our diagram. Hence, this conclusion is false.
Thus, only conclusion I follows.