Graph coloring

13.1 Assume that the color of the outer region is blue. Then we can describe what the color of a particular region $R$ is, without having to color the whole picture, as follows:

if $R$ lies inside an even number of circles, it will be colored blue;

if $R$ lies inside an odd number of circles, it will be colored red.

Prove this assertion.

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13.2 (a) Prove that the regions, into which $n$ straight lines divide the plane, are colorable with 2 colors.

(b) How could you describe what the color of a given region is?

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