Here is a refined version of the instructions with improved grammar and no unnecessary words: "Write a C function `check` that takes three `int` parameters: `x`, `y`, and `n`. The function should return `1` if `x` and `y` are both within the range from `0` to `n - 1`, inclusive. Otherwise, it should return `0`."

To write the function `check` in C that adheres to the given instructions, you can use the following code:

```c int check(int x, int y, int n) { if ((x >= 0 && x < n) && (y >= 0 && y < n)) { return 1; } else { return 0; } } ```

This function checks whether `x` and `y` are both within the range `0` to `n - 1`. If both `x` and `y` fit within this range, the function returns `1`. If either `x` or `y` (or both) does not fit within the range, the function returns `0`.

The condition `(x >= 0 && x < n)` verifies that `x` is greater than or equal to `0` and less than `n`. Similarly, `(y >= 0 && y < n)` checks the same for `y`. The use of the logical AND operator `&&` ensures that the function returns `1` only if both conditions are true.

Extra: The function provided above is an example of a simple range checking function in the C programming language. Range checking is a common task in programming, as it is frequently required to validate that input values are within expected boundaries.

In C, functions that perform checks often return integers, with a non-zero value (commonly `1`) indicating "true" or success, and `0` indicating "false" or failure. This is because C does not have a native boolean data type (in standard C89), although later standards (C99 onwards) define a `_Bool` type and a `bool` macro in `stdbool.h`.

Additionally, the concept of "inclusive" range means that the endpoints (in this case, `0` and `n - 1`) are considered part of the range, hence the `>=` and `<` operators are used for the comparison. This is in contrast with an "exclusive" range, which would not include the endpoint, and would be checked using `>` and `<` operators, for example.

Understanding how to check if values are within a certain range is essential for array indexing, loop termination, and conditional execution, all of which are foundational programming concepts. Ensuring that values are within valid ranges is also an important aspect of writing secure and robust code, as it prevents errors like buffer overflows, which can be exploited for malicious purposes or cause programs to crash.