Answer:

D. Sometimes true

Solution:

If xy < 0, then it means that the product of x and y is negative. This can happen in two cases: either x and y have opposite signs (one is positive and the other is negative), or both x and y are negative.

In the first case, if x is positive and y is negative, then x > 0 and y < 0, so the statement is true.

In the second case, if both x and y are negative, then x < 0 and y < 0, so the statement is false.

Therefore, the statement "If xy < 0, then x > 0 and y < 0" is only sometimes true.

Answer:

The statement "If xy < 0, then x > 0 and y < 0." is sometimes true.

When the product of two numbers is less than zero, it means that one of the numbers must be positive and the other must be negative. So, if xy < 0, either x is positive and y is negative, or x is negative and y is positive.

Therefore, the statement "If xy < 0, then x > 0 and y < 0." is only true when x is positive and y is negative. So, it is only sometimes true.

So, the answer is d. Sometimes true.