$3.$ AVL Trees:

$($a$)$ Let $\backslash (\backslash$mathbf$\{$T$\}\backslash )$ be the tree after Question $\backslash (2($b$)\backslash ).$ Is $\backslash (\backslash$mathbf$\{$T$\}\backslash )$ an AVL Tree?

$($b$)$ Consider the following AVL Tree: What will the tree look like after InSERT$-$AVL$(6)$ is called?

Figure $1$: Binary Search Tree

$($c$)$ What will the tree in Figure $1$ look like after Remove$-$AVL$(3)$ is called?