Which of the four statements given below is different from others?
(a) `f:AtoB` (b) `f:xtof(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 four statements is different from the others, we will analyze each statement one by one.

### Step 1: Analyze the first statement
The first statement is:
**(a) f: A to B**
This statement indicates that f is a function that maps elements from set A to set B. This is a standard way to denote a function.

**Hint:** Look for the standard notation of functions in set theory.

### Step 2: Analyze the second statement
The second statement is:
**(b) f: x to f(x)**
This statement suggests that f is a function that takes an input x and maps it to f(x). Here, x is a variable representing an element, and f(x) is the output of the function. This is a different representation but still describes a function.

**Hint:** Consider how functions can be expressed in terms of their input and output.

### Step 3: Analyze the third statement
The third statement is:
**(c) f is a mapping of A into B**
This statement explicitly states that f is a mapping (or function) that takes elements from set A and maps them into set B. This is essentially the same as the first statement but uses different wording.

**Hint:** Think about the terminology used in mathematics to describe functions and mappings.

### Step 4: Analyze the fourth statement
The fourth statement is:
**(d) f is a function of A into B**
This statement indicates that f is a function that takes inputs from set A and produces outputs in set B. This is also equivalent to the first statement.

**Hint:** Reflect on how the phrase "function of A into B" relates to the definition of a function.

### Conclusion
After analyzing all four statements:
- Statements (a), (c), and (d) are essentially equivalent, as they all describe a function mapping from set A to set B.
- Statement (b) is different because it describes a function in terms of its input-output relationship rather than directly stating the mapping between sets.

Thus, the answer is that **(b) f: x to f(x)** is the statement that is different from the others.