in rule method the null set is resresented by

Options

A. {0}
B. `Phi`
C. `{x:x ne x}`
D. `{x:x=x}`

Answer

To solve the question, "In rule method, the null set is represented by," we will analyze the options provided and determine which one correctly represents the null set using the rule method.

### Step-by-Step Solution:

1. **Understanding the Null Set**:
The null set, also known as the empty set, is a set that contains no elements. It is commonly represented in two ways: as `{}` (curly brackets) or as the symbol `∅` (phi).

2. **Analyzing the Options**:
- **Option 1**: This option likely represents a non-empty set. Since we are looking for the null set, we can eliminate this option.
- **Option 2**: Similar to option 1, this also likely represents a non-empty set. Hence, we can eliminate this option as well.
- **Option 3**: This option states "x such that x is not equal to x". This is a logical contradiction because there are no values of x that can satisfy this condition. Therefore, this set will contain no elements, making it the null set.
- **Option 4**: This option states "x such that x is equal to x". This is always true for any x, which means this will represent all possible values of x, thus it cannot represent the null set.

3. **Conclusion**:
Based on the analysis, the correct representation of the null set in the rule method is given by **Option 3: x such that x is not equal to x**.

### Final Answer:
The null set is represented by: **x such that x is not equal to x**.

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