Answer
The regions represented by the given set are Quadrants II and IV.
Work Step by Step
The product of the x and y coordinates of each point is less than zero or negative.
This product of $x$ and $y$ will be negative only when $x$ and $y$ have opposite signs.
Note that the x and y coordinates have opposite signs in Quadrant II and Quadrant IV.
Thus, the regions given by the set are Quadrant II and Quadrant IV.
