$($a$)$ Convert the following decision list into a binary decision tree. $(4)$

$$ 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. $(5)$

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

mathematical terms. $(3)$

$($d$)$ Why is Entropy used as a measure in constructing Decision Trees? $(1)$

$($e$)$ Name another measure used in constructing Decision Trees. $(1)$

$($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. $(5)$

sample S T O C

s$1$ M m f Y

s$2$ S t s Y

s$3$ L p e Y

s$4$ L p s Y

s$5$ S t l N

s$6$ L t l N

s$7$ L t e N

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

$($g$)$ Calculate the Information Gain for the T attribute in Table $4.(6)$

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

don$$t need to do any calculations$)?(1)$