State True or False: To convert the assignment problem into maximization problem, the smallest element in the matrix is to deducted from all other elements.

Answer

To determine whether the statement is true or false, we need to analyze the process of converting an assignment problem into a maximization problem.

### Step-by-Step Solution:

1. **Understanding the Assignment Problem**:
The assignment problem typically involves minimizing costs associated with assigning tasks to agents. It is represented by a cost matrix where each element represents the cost of assigning a particular task to a specific agent.

2. **Conversion to Maximization Problem**:
To convert a minimization problem into a maximization problem, we need to manipulate the cost matrix. The common method involves transforming the costs so that we can maximize the profits instead of minimizing the costs.

3. **Identifying the Correct Method**:
The correct approach to convert the assignment problem into a maximization problem is to take the largest element in the matrix and subtract each element from it. This way, the smallest costs become the largest profits.

4. **Evaluating the Statement**:
The statement claims that to convert the assignment problem into a maximization problem, the smallest element in the matrix should be deducted from all other elements. This is incorrect. Therefore, the statement is **False**.

### Final Answer:
The statement is **False**.