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))`
Find the value of `Delta(3, 2)-Delta(2, 3)+ g t (4.8)- l t(2.7)+Delta(4, 5)`

Options

A. a. 4
B. b. 5
C. c. 6
D. d. none of these

Answer

To solve the problem step by step, we will evaluate each component of the expression given in the question:

1. **Calculate Delta(3, 2)**:
- `lt(3)` is the least integer greater than or equal to 3, which is 3.
- `gt(2)` is the greatest integer less than or equal to 2, which is 2.
- Therefore, `Delta(3, 2) = Min(lt(3), gt(2)) = Min(3, 2) = 2`.

2. **Calculate Delta(2, 3)**:
- `lt(2)` is the least integer greater than or equal to 2, which is 2.
- `gt(3)` is the greatest integer less than or equal to 3, which is 3.
- Therefore, `Delta(2, 3) = Min(lt(2), gt(3)) = Min(2, 3) = 2`.

3. **Calculate gt(4.8)**:
- `gt(4.8)` is the greatest integer less than or equal to 4.8, which is 4.

4. **Calculate lt(2.7)**:
- `lt(2.7)` is the least integer greater than or equal to 2.7, which is 3.

5. **Calculate Delta(4, 5)**:
- `lt(4)` is the least integer greater than or equal to 4, which is 4.
- `gt(5)` is the greatest integer less than or equal to 5, which is 5.
- Therefore, `Delta(4, 5) = Min(lt(4), gt(5)) = Min(4, 5) = 4`.

Now, we can substitute these values back into the original expression:

\[ Delta(3, 2) - Delta(2, 3) + gt(4.8) - lt(2.7) + Delta(4, 5) \]

Substituting the values we calculated:

\[ 2 - 2 + 4 - 3 + 4 \]

Now, performing the arithmetic:

\[ 0 + 4 - 3 + 4 = 4 - 3 + 4 = 1 + 4 = 5 \]

Thus, the final result is:

\[ \Delta(3, 2) - \Delta(2, 3) + gt(4.8) - lt(2.7) + \Delta(4, 5) = 5 \]

### Final Answer:
The value is **5**.