If x - y = 8 , then which of the following must be true? 1. Both x and y must be positive for any value of x and y . 2. If x is positive, y must be negative for any value of x and y . 3. If x is negative, y must be positive for any value of x and y . Select the correct answer using the code given below

The given equation is x - y = 8. Let's analyze each statement: 1. Both x and y must be positive for any value of x and y. This is false. Consider x = 5 and y = -3. Here, x - y = 5 - (-3) = 5 + 3 = 8. In this case, y is negative. Also, consider x = -2 and y = -10. Here, x - y = -2 - (-10) = -2 + 10 = 8. In this case, both x and y are negative. 2. If x is positive, y must be negative for any value of x and y. This is false. Consider x = 10 and y = 2. Here, x - y = 10 - 2 = 8. In this case, x is positive, and y is also positive, not negative. 3. If x is negative, y must be positive for any value of x and y. This is false. From x - y = 8, we can write y = x - 8. If x is negative (e.g., x = -1), then y = -1 - 8 = -9. In this case, x is negative, and y is also negative, not positive. In fact, if x is negative, x - 8 will always be a smaller (more negative) number, so y will also be negative. Since all three statements are false, none of them must be true. Therefore, option D is the correct answer.