2. Let R = [0,1] × [0, 1] be the square with vertices (0,0), (1,0), (1, 1) and (0, 1) and let
P be the partition of R consisting of the partition $\frac{k}{2^m}$: k = 0,1,...,2$^m$ in both
factors of R. For m = 1,2, find U($x_S$, P) and L($x_S$, P) if
S = {(x, y) ? R: (2x-1)$^2$ + (2y-1)$^2$ ? 1} using the following box
For a given set S and subrectangles $R_j$,
$\sup_{R_j} x_S = \begin{cases} 1 & \text{if } R_j \cap S \neq \emptyset, \
0 & \text{if } R_j \cap S = \emptyset, \end{cases}$
$\inf_{R_j} x_S = \begin{cases} 1 & \text{if } R_j \subset S, \
0 & \text{if all other } R_j's. \end{cases}$
(a) (6 pts) For m = 1,
(b) (6 pts) For m = 2,
