a and b are any number and x and y are any non negative integers.
`f(a)=` the greatest integer less than or equal to a
`g(a)=` the smallest integer greater than or equal to a `r(x, y)=` the remainder when x is dividied by y.
`r((16, 7)-2` is equal to :

Options

A. 0
B. 1
C. 2
D. 3

Answer

To solve the problem `r(16, 7) - 2`, we will follow these steps:

### Step 1: Calculate r(16, 7)
The function `r(x, y)` represents the remainder when `x` is divided by `y`. Here, we need to find `r(16, 7)`.

- When we divide `16` by `7`, we can express it as:
\[ 16 = 7 \times 2 + r \]
where `r` is the remainder.

- Calculating `7 \times 2` gives us `14`.

- Now, we subtract `14` from `16` to find the remainder:
\[ r = 16 - 14 = 2 \]

So, we have:
\[ r(16, 7) = 2 \]

### Step 2: Subtract 2 from the result
Now we need to compute:
\[ r(16, 7) - 2 \]
Substituting the value we found:
\[ 2 - 2 = 0 \]

### Final Result
Thus, the final answer is:
\[ \boxed{0} \]

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