$($a$)$ Using the dataset in the table below, determine the information gain of each of the features and identify the root node $(9$ marks$)$

$\backslash$table$[[$Day$,$outlook,temperature,humidity,wind,playtennis$],[$D$1,$sunny,hot,high,weak,no$],[$D$2,$sunny,hot,high,strong,no$],[$D$3,$overcast,hot,high,weak,yes$],[$D$4,$rain,mild,high,weak,yes$],[$D$5,$rain,cool,normal,weak,yes$],[$D$6,$rain,cool,normal,strong,no$],[$D$7,$overcast,cool,normal,strong,yes$],[$D$8,$sunny,mild,high,weak,no$],[$D$9,$sunny,cool,normal,weak,yes$],[$D$10,$rain,mild,normal,weak,yes$],[$D$11,$sunny,mild,normal,strong,yes$],[$D$12,$overcast,mild,high,strong,yes$],[$D$13,$overcast,hot,normal,weak,yes$],[$D$14,$rain,mild,high,strong,no$]]$

Training examples for the target concept "PlayTennis"

$($b$)$ Overfitting has been identified as one of the main issues of Decision Tree algorithm and pruning has also been identified as one of the main approaches in reducing overfitting. Describe what you understand by pruning and identify the stages pruning can be applied. $(3$ marks$)$

$($c$)$ One of the issues faced by Decision Tree Algorithm is the problem of missing attributes. List three $(3)$ methods of handing the problem of missing attributes $(3$ marks$)$