If `(p)rarr` the least possible integer greater than or equal to p.
`g t (p)rarr` the greatest possible integer less than or equal to p.
`Delta(p, q) =Min (l t(p), g t(q))`
What is the vlaue of lt `(8.3)-g t(5.3)+l t(6.8)+g t(9.4)`

Options

A. 15
B. 20
C. 19
D. none of these

Answer

To solve the problem, we need to evaluate the expression \( lt(8.3) - gt(5.3) + lt(6.8) + gt(9.4) \) using the definitions provided.

### Step-by-Step Solution:

1. **Calculate \( lt(8.3) \)**:
- The least possible integer greater than or equal to \( 8.3 \) is \( 9 \).
- Therefore, \( lt(8.3) = 9 \).

2. **Calculate \( gt(5.3) \)**:
- The greatest possible integer less than or equal to \( 5.3 \) is \( 5 \).
- Therefore, \( gt(5.3) = 5 \).

3. **Calculate \( lt(6.8) \)**:
- The least possible integer greater than or equal to \( 6.8 \) is \( 7 \).
- Therefore, \( lt(6.8) = 7 \).

4. **Calculate \( gt(9.4) \)**:
- The greatest possible integer less than or equal to \( 9.4 \) is \( 9 \).
- Therefore, \( gt(9.4) = 9 \).

5. **Substitute the values into the expression**:
- Now we substitute the values we calculated into the expression:
\[ lt(8.3) - gt(5.3) + lt(6.8) + gt(9.4) = 9 - 5 + 7 + 9 \]

6. **Perform the arithmetic**:
- First, calculate \( 9 - 5 = 4 \).
- Then, add \( 7 \): \( 4 + 7 = 11 \).
- Finally, add \( 9 \): \( 11 + 9 = 20 \).

### Final Result:
The value of the expression \( lt(8.3) - gt(5.3) + lt(6.8) + gt(9.4) \) is \( 20 \).