Let `forall` be an operation on a defined as `forall`a=`(a^(2)-3a-4)`. If `forall`k also equals (k-4),find the positive value of k.

Answer

To solve the problem, we need to find the positive value of \( k \) such that the operation \( \forall k \) defined as \( k^2 - 3k - 4 \) is equal to \( k - 4 \).

### Step-by-Step Solution:

1. **Define the operation**:
We know that \( \forall a = a^2 - 3a - 4 \). Therefore, for \( k \):
\[ \forall k = k^2 - 3k - 4 \]

2. **Set up the equation**:
According to the problem, we also have:
\[ \forall k = k - 4 \]
Therefore, we can set the two expressions equal to each other:
\[ k^2 - 3k - 4 = k - 4 \]

3. **Rearranging the equation**:
To solve for \( k \), we will rearrange the equation. First, subtract \( k \) and add \( 4 \) to both sides:
\[ k^2 - 3k - 4 - k + 4 = 0 \]
Simplifying this gives:
\[ k^2 - 4k = 0 \]

4. **Factoring the equation**:
We can factor out \( k \):
\[ k(k - 4) = 0 \]

5. **Finding the roots**:
Setting each factor equal to zero gives us:
\[ k = 0 \quad \text{or} \quad k - 4 = 0 \implies k = 4 \]

6. **Identifying the positive value**:
The problem asks for the positive value of \( k \). Therefore, the positive solution is:
\[ k = 4 \]

### Final Answer:
The positive value of \( k \) is \( \boxed{4} \).