Decision Tree algorithm $(4$ points$).$

a$.$ Find entropy $\backslash (\backslash$mathrm$\{$H$\}(\backslash$mathrm$\{$s$\})\backslash )(\backslash (\backslash$mathbf$\{1\}\backslash )$ point$)$ and information gain $(\backslash (\backslash$mathbf$\{1\}\backslash )$ point$)$ for each attribute to find the best attribute to split on for the following dataset. The dataset has $14$ samples with $4$ attributes and $1$ result $($Class$).$

$\backslash$begin$\{$tabular$\}\{|$l$|$l$|$l$|$l$|$l$|\}$

$\backslash$hline Industry & Job Type & Income & $\backslash$begin$\{$tabular$\}\{$l$\}$

Previous $\backslash \backslash$

Customer

$\backslash$end$\{$tabular$\}$ & Class $\backslash \backslash$

$\backslash$hline Aerospace & Engineering & High & No & NO $\backslash \backslash$

$\backslash$hline Aerospace & Engineering & High & Yes & NO $\backslash \backslash$

$\backslash$hline Auto & Engineering & High & No & YES $\backslash \backslash$

$\backslash$hline Electronics & Marketing & High & No & YES $\backslash \backslash$

$\backslash$hline Urban & Marketing & Low & No & YES $\backslash \backslash$

$\backslash$hline Urban & Marketing & Low & Yes & NO $\backslash \backslash$

$\backslash$hline Auto & Marketing & Low & Yes & YES $\backslash \backslash$

$\backslash$hline Aerospace & Sales & High & No & NO $\backslash \backslash$

$\backslash$hline Aerospace & Marketing & Low & No & YES $\backslash \backslash$

$\backslash$hline Electronics & Sales & Low & No & NO $\backslash \backslash$

$\backslash$hline Aerospace & Sales & Low & Yes & YES $\backslash \backslash$

$\backslash$hline Electronics & Sales & High & Yes & NO $\backslash \backslash$

$\backslash$hline Auto & Engineering & Low & No & YES $\backslash \backslash$

$\backslash$hline Electronics & Sales & High & Yes & NO $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

b$.$ Draw the whole decision tree including entropy, information gain, and outcomes $($Yes$/$No$)$ for each node $(6$ points$)$