Question 1: (10 marks)
Draw the following sets (1 mark each) and decide if they're open, closed,
neither open nor closed, or both open and closed. (1 mark each)
i. $B(\left(-\frac{1}{1}\right), 2)$
ii. $(-\infty, 2) \times (3, \infty)$
iii. $([-1, 0) \cup (1, 3]) \times ([-1, 0) \cup (1, 3])$
iv. $B(\left(-\frac{1}{1}\right), 2) \cup B((0), 2)$
v. $\{(x, y)^T | x^2 + y^2 < 4 \text{ and } x > 1\}$.
Question 2: (5 marks)
For each of the sets in Question 1, determine its diameter ($\frac{1}{2}$ mark), and
whether or not (Yes/No) the diameter of that set can be realised as the dis-
tance between two points in that set ($\frac{1}{2}$ mark).