Consider te following
I. New Delhi is in Nepal.
II. Every relation is a function. III. Do your homework.
Choose the correct option.

Options

A. I and II are statements.
B. I and III are statements.
C. II and III are statements.
D. I,II and III are statements.

Answer

To solve the given question, we need to analyze each of the three sentences provided and determine whether they qualify as statements based on the definition of a statement in mathematical reasoning.

### Step-by-Step Solution:

1. **Identify the Definition of a Statement**:
A statement is defined as a declarative sentence that can be classified as either true or false, but not both.

2. **Analyze Sentence I: "New Delhi is in Nepal."**:
- This sentence can be evaluated for its truth value.
- The statement is actually false because New Delhi is the capital of India, not Nepal.
- Since it can be classified as false, it qualifies as a statement.

3. **Analyze Sentence II: "Every relation is a function."**:
- This sentence can also be evaluated for its truth value.
- This statement is false because not all relations are functions; a function must have a unique output for each input.
- Since it can be classified as false, it qualifies as a statement.

4. **Analyze Sentence III: "Do your homework."**:
- This sentence is an imperative or command.
- It does not have a truth value; it cannot be classified as true or false.
- Therefore, it does not qualify as a statement.

5. **Conclusion**:
- From the analysis, we find that:
- Sentence I is a statement (false).
- Sentence II is a statement (false).
- Sentence III is not a statement.
- Thus, the correct option is that only the first two sentences are statements.

### Final Answer:
The correct option is that only the first two sentences (I and II) are statements.

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