1.

(a) Let a::; band c ::; d be real numbers. Sketch a graph of the rectangle

[a, b] x [c, dj := {(x, y) : x E [a, b], y E [c, dj}

and decide whether this set is compact or connected. Explain your answers.

(b) Sketch a graph of the set B1(-2,0) U B1(2,0) U {(x, 0) : -1 < x < I}

and decide whether this set is compact or connected. Explain your answers.