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.