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.