Consider the metric space $(E, d)$ where $E = [0, 1] \cup [2, 4)$ and \\
for all $x, y \in E$. \\
d(x, y) = |x - y| \\
(a) Is $A = [2, 4)$ open in $(E, d)$? \\
(b) Is $A = [2, 4)$ closed in $(E, d)$? \\
(c) Show that $B = [0, 1]$ is closed in $(E, d)$. \\
(d) Does the sequence $x_n = 4 - 3^{-n}$ converge in $(E, d)$?