Question

Please help!! I have no idea how to do this!

Let x and y be numbers such that

-y
Which of the following must be true?

I. |x|
II. x>0
III. y>0


A) I only

B) I and II only

C) I and III only

D) I, II, and III

Answer 1

1. Is true. If you think about it, -y < x, right? Therefore, on both sides, no matter positive or negative, |x| must always be < y
2. Is not true. We can have the example y = 5 and x = -3. In this case, the statement would be true: -5 < -3 < 5, but -3 is not larger than 0.
3. Is not true. We have have the example y = -2 and x = 1 . In this case, 2 < 1 but 1 cannot be smaller than a negative number.

Therefore, the answer is A