Question $3$: Decision trees

$($a$)$ Convert the following decision list into a binary decision tree.

if $A=0$ then $1$

else if $B=0$ then $1$

else $0$

$($b$)$ Write down the truth table for the decision list in $($a$),$ and derive a Boolean

function from the truth table.

$($c$)$ What is meant by the term entropy? Define the entropy of a data set $S$ in

mathematical terms.

$($d$)$ Why is Entropy used as a measure in constructing Decision Trees?

$($e$)$ Name another measure used in constructing Decision Trees.

$($f$)$ Calculate Entropy $(C)$ for the data in the Table $4.$ Show your assumptions

and define your notation clearly $($use the Table on p$.7$ in your calculations$).$

Show all your calculations.

Table $4$: Objects with attributes and their classification as $C(Y,N).$

$($g$)$ Calculate the Information Gain for the $T$ attribute in Table $4.$

$($h$)$ Which attribute would be used for the root node of the decision tree $($HINT: you

don't need to do any calculations$)?$