Question $4-$ PAC, VC dimension, Bias vs Variance

Section $1$

A circle $(r,c)$ is defined by its center $c$ and its radius $r.$ Look at the following classifiers family:

$H=\{h_{r,c}$:rinR,$cin{R}^2\}$ where $h_{r,c}(x)=1$ iff $x$ inside the circle $(r,c)$

Find the VCdim of this class with full proof.

Section $2$

Consider a training set $S=\{(x_1,y_1),$dots,$(x_n,y_n)\}$ where $x_{i}in\{0,1{\}}^3.$ In other words, each sample has $3$ Boolean features $\{x_1,x_2,x_3\}.$ You are also given the classification rule $Y=(x_1^{{?}^{?}}{x}_2)vv(not{x}_1^{{?}^{?}}not{x}_2).$

We try to learn the function $f$:$xY$ using a "depth $1$ decision trees". A "depth$-1$ decision tree" is a tree with two leaves, all distance $1$ from the root.

Analyze this problem and decide the appropriate sample complexity formula. Justify your answer.

Section $3$

Dana was given a hard classification problem and she decided to use SVM with polynomial kernel with $d=2,10,20.$ For each degree, she tried $15$ to $85$ training samples, with jumps of $.$