Problem $5$: $(15$ points$)$

a$)$ Draw an almost complete binary tree of $13$ nodes, and a perfect ternary tree of height $2.$

b$)$ Draw a B$-$tree of order $4,$ where the height is $2$ and the number of nodes is at least $17$ and at most $20.$

c$)$ Consider a B$-$tree of order $m$ and height $h,$ where the root has $r$ children, and the total number of nodes is $n.$ Prove that $n1+r\frac{m^h-1}{m-1}.$

d$)$ Let $T$ be a binary tree of $n$ nodes and height $h.$ Prove that the number of leaves is $2^h,$ and that $n{2}^{h+1}-1.$

PLEASE SHOW UR WORK FOR THIS I UAVE NO CLUE.