`xy gt 0`
`{:("Quantity A","Quantity B"),(x+y,0):}`

Options

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the infromation given.

Answer

To solve the problem, we need to analyze the relationship between \( x + y \) (Quantity A) and \( 0 \) (Quantity B) given the condition \( xy > 0 \).

### Step-by-Step Solution:

1. **Understanding the Condition**:
The condition \( xy > 0 \) implies that both \( x \) and \( y \) must either be positive or both must be negative. This is because the product of two numbers is positive if both numbers are either positive or negative.

2. **Case 1: Both \( x \) and \( y \) are Positive**:
- Let’s assume \( x = 1 \) and \( y = 2 \).
- Then, \( xy = 1 \times 2 = 2 \), which is greater than \( 0 \).
- Now, calculate \( x + y \):
\[ x + y = 1 + 2 = 3 \]
- Compare \( x + y \) with \( 0 \):
\[ 3 > 0 \]
- In this case, Quantity A (3) is greater than Quantity B (0).

3. **Case 2: Both \( x \) and \( y \) are Negative**:
- Let’s assume \( x = -1 \) and \( y = -2 \).
- Then, \( xy = (-1) \times (-2) = 2 \), which is also greater than \( 0 \).
- Now, calculate \( x + y \):
\[ x + y = -1 + (-2) = -3 \]
- Compare \( x + y \) with \( 0 \):
\[ -3 < 0 \]
- In this case, Quantity A (-3) is less than Quantity B (0).

4. **Conclusion**:
- From Case 1, we found that \( x + y > 0 \).
- From Case 2, we found that \( x + y < 0 \).
- Since we have two different scenarios yielding different results for \( x + y \) in relation to \( 0 \), we conclude that the relationship between Quantity A and Quantity B cannot be determined.

### Final Answer:
The answer is that the relationship cannot be determined.