6.

(a) Sketch a graph of the set U := {(x, y) : X2 + 2y2 < 6, y ~ O}, and decide whether this set is relatively open or relatively closed in E :=

{(x,y) : y ~ O}. Do the same for E:= {(x,y) : x2 + 2y2 < 6}. Explain your answers.

(b) Sketch a graph of set U : = {(x, y) : x2 + y2 :s 1, x2 - 4x + y2 + 2 < O}, and decide whether this set is relatively open or relatively closed in the closed ball E centered at (0,0) of radius l. Do the same for E := B.j2(2, 0). Explain your answers.