Directions :In each group of question below are two conclusions follo...
Conclusions:
1. At least some states are district.
2. Some towns being district is a possibility.
Statements:
I. All districts are states. Some states are village. No town is district.
II. No districts is states. Some states are towns. No town is village.
III. All districts are states. Some states are towns. No town is village.
IV. No districts is states. Some states are towns. No town is village.
V. All districts are states. Some states are village. Some town are village.
Solution:
To satisfy the given conclusions, we need to find a set of statements that guarantees the existence of both district states and the possibility of some towns being districts.
Statement I:
- All districts are states. Some states are village. No town is district.
This statement does not guarantee the existence of district states, as it states that no town is a district. So, it does not satisfy the first conclusion.
Statement II:
- No districts is states. Some states are towns. No town is village.
This statement also does not guarantee the existence of district states, as it states that no district is a state. So, it does not satisfy the first conclusion.
Statement III:
- All districts are states. Some states are towns. No town is village.
This statement satisfies both conclusions. It states that all districts are states, which guarantees the existence of district states. It also states that some states are towns, which satisfies the possibility of some towns being districts. Additionally, it states that no town is a village, which is not relevant to the given conclusions.
Statement IV:
- No districts is states. Some states are towns. No town is village.
This statement does not guarantee the existence of district states, as it states that no district is a state. So, it does not satisfy the first conclusion.
Statement V:
- All districts are states. Some states are village. Some town are village.
This statement satisfies both conclusions. It states that all districts are states, which guarantees the existence of district states. It also states that some states are villages, which satisfies the possibility of some towns being districts. Additionally, it states that some towns are villages, which is not relevant to the given conclusions.
Therefore, the correct set of statements that logically satisfies the given conclusions is Statements III and V.
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