Sketch each of the following sets. Identify which of the following sets are open, which are closed, and which are neither. Also discuss the connectivity of each set.
a) E = {(x, y): y ≠ 0}
b) E = {(x, y): x2 + 4y2 < 1}
c) E = {(x, y): y > x2, 0 < y < 1}
d) E = \(x, y): x2 - y2 > 1, -1 < y < 1}
e) E = [lx, y): x2 - 2x + y2 = 0} U {(x, 0) : x ∈ [2, 3]}