Solve the following questions on the basis of the following questions on the basis of following functions
(a) `P_((n+1))=P_((n))-P_((n-1)),P` is the term of the sequence and `P_((0))=0, P_((1))=1`
(b) `Q_((n+1))=Q_((n))+Q_((n+1)),Q` is the term of the sequence and `Q_((0))=0, Q_((1))=1`
The value of P cannot be :

Options

A. `-1
B. 0
C. 1
D. 4

Answer

To solve the given problem, we will analyze the sequences defined by the functions provided and determine the possible values of \( P_n \).

### Step-by-step Solution:

1. **Define the Sequence \( P_n \)**:
The recursive formula given is:
\[ P_{n+1} = P_n - P_{n-1} \]
with initial conditions:
\[ P_0 = 0, \quad P_1 = 1 \]

2. **Calculate the Terms of the Sequence**:
- **Calculate \( P_2 \)**:
\[ P_2 = P_1 - P_0 = 1 - 0 = 1 \]
- **Calculate \( P_3 \)**:
\[ P_3 = P_2 - P_1 = 1 - 1 = 0 \]
- **Calculate \( P_4 \)**:
\[ P_4 = P_3 - P_2 = 0 - 1 = -1 \]
- **Calculate \( P_5 \)**:
\[ P_5 = P_4 - P_3 = -1 - 0 = -1 \]
- **Calculate \( P_6 \)**:
\[ P_6 = P_5 - P_4 = -1 - (-1) = 0 \]
- **Calculate \( P_7 \)**:
\[ P_7 = P_6 - P_5 = 0 - (-1) = 1 \]
- **Calculate \( P_8 \)**:
\[ P_8 = P_7 - P_6 = 1 - 0 = 1 \]
- **Calculate \( P_9 \)**:
\[ P_9 = P_8 - P_7 = 1 - 1 = 0 \]

3. **Observe the Pattern**:
The calculated terms of the sequence \( P_n \) are:
\[ P_0 = 0, \quad P_1 = 1, \quad P_2 = 1, \quad P_3 = 0, \quad P_4 = -1, \quad P_5 = -1, \quad P_6 = 0, \quad P_7 = 1, \quad P_8 = 1, \quad P_9 = 0 \]
The values oscillate between 1, 0, and negative values. Notably, the sequence does not yield any positive values beyond \( P_1 \).

4. **Conclusion**:
From the calculations, we see that \( P_n \) can take the values 1, 0, and negative integers, but it never reaches 4. Therefore, the value of \( P \) cannot be 4.

### Final Answer:
The value of \( P \) cannot be: **4**.