Answer
a) No
b) Yes
c) Yes
Work Step by Step
a) For the open set, the region should not contain any boundary points. When we draw a disk for the given set, we find that it does not entirely lie inside the region $D$. Thus, the set is not open.
b) For the connected set, any two points in the region $D$ can be connected by a path that lies entirely in the region $D$. From the given points we can draw a path connecting the two points in the region $D$. Thus, the set is connected.
c) For the simply connected set, the region must not have any holes or be divided into two parts. From the given points, it has been seen that the path connecting the two points completely lie inside the given set. Thus, the set is simply connected.
