Which of the following is an open statement?

Options

A. x is a natural number
B. Give me a glass of water
C. Wish you best of luck
D. Good morning to all

Answer

To determine which of the given options is an open statement, we first need to understand the definitions of a statement and an open statement.

### Step-by-Step Solution:

1. **Definition of a Statement**:
A statement is a declarative sentence that is either true or false, but not both. For example, "The sky is blue" is a statement because it can be verified as true or false.

2. **Definition of an Open Statement**:
An open statement is a sentence that contains a variable and can be either true or false depending on the value of that variable. For instance, "x is a natural number" is an open statement because its truth depends on the value assigned to x.

3. **Analyzing the Options**:
We need to analyze the given options to see which one qualifies as an open statement.

- **Option 1**: "x is a natural number"
- This is an open statement because the truth of this statement depends on the value of x. If x = 1, the statement is true; if x = 1.1, the statement is false.

- **Option 2**: "2 + 2 = 4"
- This is a true statement as it is always true regardless of any variable.

- **Option 3**: "The Earth is flat"
- This is a false statement as it is definitively false.

- **Option 4**: "All cats are mammals"
- This is a true statement as it is universally true.

4. **Conclusion**:
Among the options, only "x is a natural number" is an open statement because it can be true or false based on the value of x. The other options are definitive statements that are either true or false without any variable.

### Final Answer:
The open statement is **Option 1: "x is a natural number."**