What are the inequalities that define the region in the first quadrant? How about 2nd, 3rd and 4th quadrants?

Quadrant 1 - positive x and positive y coordinates
Quadrant 2 - negative x but positive y coordinates
Quadrant 3 - negative x and negative y coordinates
Quadrant 4 - positive x but negative y coordinates

This is the information that I came up with but I am not sure if I am understanding the question completely.

You just have to express it differently: x>0;y>0 or 0<x<=inf; 0<y<=inf

Just express positive x, positive y, negative x and negative y algebraically. Positive x --> x > 0. The others fall into place similarly.