Consider the instance space of a Euclidean $2$D plane. Let us suppose that hypotheses are

represented by a circle formalized as $(a,b),r,$ where $(a,b)$ is the circle's center point, $r$ is the

radius of the circle and $a,$bin$\{-5,-4,$dots,$0,$dots,$4,5\}$ and rin$\{1,2,$dots,$10\}.$ The hypothesis is

interpreted such that all points on or within the circle are positive and points outside the circle are

negative. Suppose our data set consists of the following. Positive points: $(0,0),(1,0),(\frac{1}{2},-\frac{1}{2})$;

Negative points: $(2,3),(4,-1),(-1,4),(-3,1).$ List all the maximally specific hypotheses

and all the maximally general hypotheses in the version space. Sketch the data set as well as

these hypotheses.

$h_a(x_1)=h_a(x_2)=h_a(x_4)=h_a(x_5)=1$

$h_a(x_3)=h_a(x_6)=0$

$h_b(x_4)=h_b(x_5)=1$

$h_b(x_1)=h_b(x_2)=h_b(x_3)=h_b(x_6)=0$