$VC$ dimension $(20pts)$

Let $x=R$ and ninN.

Define $"$x$-$node decision tree" for any $x=2^n-1$ to be a full binary decision tree with $x$

nodes $($including the leaves$).$

Let $H_m$ be the hypothesis space of all $"x-$node decision tree" with $nm.$

a$.(5$ pts$)$ What is the $VC(H_3)?$ Prove your answer.

b$.(15$ pts$)$ What is the $VC(H_m)?$ Prove your answer.