`{:("Column A","For any positive ineger n, "pi(n) " represents the number of factors of n, inclusive of 1 and itself. a and b are unequal prime numbers. ","ColumnB"),(pi(a) + pi(b),,pi(a xx b)):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to analyze the two columns based on the definitions provided.

### Step-by-Step Solution:

1. **Understanding the Function \( \pi(n) \)**:
- The function \( \pi(n) \) represents the number of factors of \( n \), including 1 and \( n \) itself.

2. **Identifying the Values in Column A**:
- Column A is given as \( \pi(a) + \pi(b) \), where \( a \) and \( b \) are unequal prime numbers.
- Since \( a \) and \( b \) are prime, each has exactly two factors: 1 and itself.
- Therefore, \( \pi(a) = 2 \) and \( \pi(b) = 2 \).
- Thus, \( \pi(a) + \pi(b) = 2 + 2 = 4 \).

3. **Identifying the Values in Column B**:
- Column B is given as \( \pi(a \times b) \).
- Since \( a \) and \( b \) are prime, the product \( a \times b \) will have the factors: 1, \( a \), \( b \), and \( a \times b \).
- Therefore, \( \pi(a \times b) = 4 \) because there are four factors.

4. **Comparing Column A and Column B**:
- From our calculations, we have:
- Column A: \( \pi(a) + \pi(b) = 4 \)
- Column B: \( \pi(a \times b) = 4 \)
- Thus, both columns are equal.

5. **Conclusion**:
- Since both columns are equal, the answer to the question is that Column A is equal to Column B.

### Final Answer:
- The correct option is that the columns are equal.