Consider the statement p: 'New Delhi is a city'. Which of the following is not negation of p?

Options

A. New delhi is not a city
B. it is false that new delhi is a city
C. it is not case that New delhi is a city
D. None of these

Explanation

To solve the problem, we need to identify which of the given statements is not a negation of the statement \( p: \) "New Delhi is a city."

### Step-by-Step Solution:

1. **Understanding the Statement \( p \)**:
- The original statement \( p \) is "New Delhi is a city." This is a simple declarative statement.

2. **Defining Negation**:
- The negation of a statement is what makes the statement false. For a statement \( p \), its negation \( \neg p \) would be "New Delhi is not a city."

3. **Analyzing the Options**:
- We need to evaluate the provided options to see which one does not represent the negation of \( p \).

4. **Option 1**: "New Delhi is not a city."
- This is a direct negation of \( p \). Therefore, it is a valid negation.

5. **Option 2**: "It is false that New Delhi is a city."
- This also negates \( p \) because if it is false that New Delhi is a city, then it implies that New Delhi is not a city. Thus, this is a valid negation.

6. **Option 3**: "It is not the case that New Delhi is a city."
- This statement also negates \( p \) by saying that it is not true that New Delhi is a city, which again implies that New Delhi is not a city. Hence, this is also a valid negation.

7. **Conclusion**:
- Since all the given options are valid negations of the statement \( p \), we conclude that there is no option provided that is not a negation of \( p \).

### Final Answer:
All the given options are negations of \( p \). Therefore, there is no option that is not a negation of \( p \).

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