a and b are any numbers and x and y are any non negative integers.
l(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 divided by y.
r(16, 7)-2 is equal to :

Options

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

Answer

To solve the problem, we need to calculate \( r(16, 7) - 2 \).

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

To find the remainder of \( 16 \) divided by \( 7 \):
- Divide \( 16 \) by \( 7 \):
\[ 16 \div 7 = 2 \quad \text{(since \( 7 \times 2 = 14 \))} \]
- Now, subtract \( 14 \) from \( 16 \) to find the remainder:
\[ 16 - 14 = 2 \]
Thus, \( r(16, 7) = 2 \).

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

### Final Answer
The final result is:
\[ r(16, 7) - 2 = 0 \]