Question $4$ Let

X

be an instance space consisting of points in the Euclidian plane with integer coordinates

$($x$,$y$)$

$,$ with positive and negative instances as shown in Figure $1.$ V

$$

Positive instances: $\backslash [\backslash$begin$\{$array$\}\{$c$\}(5,5)\backslash \backslash (-6,4)\backslash \backslash (-3,-4)\backslash \backslash (2,-4)\backslash$end$\{$array$\}\backslash ]$

$$

Negative instances: $\backslash [\backslash$begin$\{$array$\}\{$c$\}(-1,2)\backslash \backslash (-2,0)\backslash \backslash (6,7)\backslash \backslash (8,-8)\backslash$end$\{$array$\}\backslash ]$ Figure $1$: Instance space with positive and negative instances. Let

H

be the set of hypotheses consisting of origin$-$centered donuts. Formally, the donut hypothesis has the form

h$$a$<$

x

$2$

$+$y

$2$

$$