Final answer:
The property that must be satisfied for the rectangle U to be a convex set is that every line segment between any two points in U lies entirely within U.
Step-by-step explanation:
To show that the rectangle U={(x,y)∥0≤x≤2,0≤y≤3} is a convex set, a specific property must be satisfied. In mathematics, a set is considered convex if, for any two points within the set, the line segment connecting these points is entirely contained within the set. In the case of rectangle U, we must demonstrate this property.
For rectangle U, any two points chosen will create a line segment that lies wholly within the bounds of the rectangle, as the x and y coordinates of these points will always satisfy the inequality constraints (0≤x≤2 and 0≤y≤3). This means that the property which must be satisfied to show that U is a convex set is the one stating that every line segment between any two points in U lies entirely within U.