$13.$ The binary Fibonacci tree Fn$,$ for a natural number n is defined recursively as follows.

$$ Base Step: F$0$ and F$1$ are both the binary tree consisting of a single vertex.

$$ Recursive Step: For n $>=2$ the rooted tree Fn is defined as the binary tree that has Fn$1$ as its

left subtree and Fn$2$ as its right subtree.

$($a$)$ Draw the first eight Fibonacci trees.

$($b$)$ How many leaves does Fn have? Prove your answer.

$($c$)$ How many internal vertices does Fn have? Prove your answer.

$($d$)$ How many vertices does Fn have? Prove your answer.

$($e$)$ What$$s the height of Fn$?$ Prove your answer. please prove with induction for b$,$c$,$d nd e