Question

Determine whether or not the given set is open, connected, and simply-connected. (Select all that apply.) (x, y) | 16 ≤ x2 + y2 ≤ 25, y ≥ 0 open connected simply-connected

Answer 1

Answer:

The set is closed, connected and simyple connected

Step-by-step explanation:

A set is closed if contains all the point in its boundaries. A set is open if it doesn't contain any of the points in its boundaries. In this set, all the points of the boundaries are included because it is using the less than or equal to and greater than or equal to define the set.

The set is connected if you can find a path inside the set to connect any two points of the set. If you make the graph of the set you would see the set covers this condition because the set hasn't any division.

The set is simply connected if you can draw a closed curve inside the set and in the interior of the curve there are only points of the set. In other words, if the set has holes is not simply connected. This set doesn't have holes, it's simply connected.