Below are given statements. You have to take the given statement to be true even if they seem to be at variance with commonly known facts decide which of the given conclusions logically follows from the given statements .
Statements :
I. All rats are hills
II. All hills are rivers.
Conclusions:
A. Some rivers are rats
B. No river is a hill
C. All hills are rats
D. No river is a rat

Options

A. C
B. B
C. D
D. A

Answer

To solve the problem, we will analyze the given statements and conclusions step by step.

### Step 1: Understand the Statements
1. **Statement I**: All rats are hills.
2. **Statement II**: All hills are rivers.

### Step 2: Draw a Venn Diagram
- Draw three circles:
- Circle A for "Rats"
- Circle B for "Hills"
- Circle C for "Rivers"

- According to Statement I, the entire circle of "Rats" (A) is contained within the circle of "Hills" (B).
- According to Statement II, the entire circle of "Hills" (B) is contained within the circle of "Rivers" (C).

### Step 3: Analyze the Conclusions
Now, let's evaluate each conclusion based on the Venn diagram.

#### Conclusion A: Some rivers are rats.
- Since all rats are hills and all hills are rivers, it logically follows that some rivers must be rats.
- **Conclusion A is true.**

#### Conclusion B: No river is a hill.
- This conclusion contradicts Statement II, which states that all hills are rivers. Therefore, it is not true that no river is a hill.
- **Conclusion B is false.**

#### Conclusion C: All hills are rats.
- This conclusion is incorrect because while all rats are hills, not all hills are rats. There are hills that are not rats.
- **Conclusion C is false.**

#### Conclusion D: No river is a rat.
- This conclusion is also false. Since all rats are hills and all hills are rivers, it means that some rivers are indeed rats.
- **Conclusion D is false.**

### Step 4: Final Decision
From the analysis, we find that only Conclusion A logically follows from the given statements.

### Answer:
The correct conclusion is **A. Some rivers are rats.**

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