Which of the statements given below is different from the other?

Options

A. `f : A to B `
B. `f : x to f(x)`
C. f is a mapping of A into B
D. f is a function of A into B

Answer

To determine which of the statements is different from the others, we need to analyze each option carefully.

### Step-by-Step Solution:

1. **Understanding the Statements**:
- We have four statements regarding functions and mappings.
- The goal is to identify which one does not fit with the others.

2. **Analyzing Each Statement**:
- **Statement 1**: F: A → B
- This indicates that F is a function that maps elements from set A to set B.
- This is a correct representation of a function.

- **Statement 2**: F: x → f(x)
- Here, 'x' is an element, and 'f(x)' represents the image of 'x' under the function F.
- This is not a proper representation of a function between two sets, as it uses lowercase letters which typically denote elements, not sets.

- **Statement 3**: F is a mapping of A into B
- This is another way of stating that F is a function from set A to set B.
- This is a correct representation of a function.

- **Statement 4**: F is a function of A into B
- Similar to Statement 3, this indicates that F is a function mapping elements from A to B.
- This is also a correct representation of a function.

3. **Identifying the Odd Statement**:
- Statements 1, 3, and 4 correctly describe functions or mappings between sets A and B.
- Statement 2 is different because it incorrectly uses lowercase letters to denote elements instead of sets, making it an improper representation of a function.

4. **Conclusion**:
- The statement that is different from the others is **Statement 2**: F: x → f(x).

### Final Answer:
The different statement is **Statement 2**: F: x → f(x).