First, please compute the: $(1)$ entropy; $(2)$ Gini; $(3)$ classification error of cases $($a$)$ and $($b$).$ Assume they are data at a node of decision tree.

a$.$ C$0$: $8$ and C$1$: $12$

b$.$ C$0$: $6$ and C$1$: $14$

Second, assume we plan to split the data for case $($a$)$ and $($b$)$ in the follow ways. Could you calculate the information gain for each? Do you suggest a split based on these, and why?

a$.$ C$0$:$1$ and C$1$:$9+$ C$0$: $7$ and C$1$:$3$

b$.$ C$0$:$3$ and C$1$:$3+$ C$0$: $3$ and C$1$:$11$