Suppose we modified Example $12\mathrm{.}11$ to look at the two nearest neighbors of a query point q$.$ Classify q with the common label if those two neighbors have the same label, and leave q unclassified if the labels of the neighbors are different.

$($a$)$ Sketch the boundaries of the regions for the three dog breeds on Fig. $12\mathrm{.}21.$

$($b$)$ Would the boundaries always consist of straight line segments for any training data?