Which one of the following is a null set ?

Options

A. {0}
B. {{{}}}
C. {{}}
D. `{x|x^2+1=0, x epsilon R}`

Answer

To determine which of the given options is a null set, we first need to understand what a null set is. A null set, also known as an empty set, is a set that contains no elements.

### Step-by-Step Solution:

1. **Understand the Definition of Null Set**:
- A null set is defined as a set that has no elements. It is denoted by the symbol ∅ or {}.

2. **Analyze the Options**:
- We need to look at the options provided in the question. Since the options are not given here, we will assume that they include various sets.

3. **Identify the Set with No Elements**:
- For each option, check if it contains any elements. If an option is empty or does not contain any elements, it is a null set.

4. **Example Analysis**:
- For example, consider the equation \(x^2 + 1 = 0\).
- Rearranging gives \(x^2 = -1\).
- Since there are no real numbers \(x\) that satisfy this equation (as the square of a real number cannot be negative), the solution set is empty.

5. **Conclusion**:
- Based on the analysis, the option that corresponds to an empty set is the null set. In this case, if option number 4 represents the empty set, then option number 4 is the correct answer.

### Final Answer:
- The null set among the options is option number 4.

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