prove the following statement using induction. for full credit, $do$ not forget $to$ state the conclusion $of$ your proof and the type $of$ induction you used.

$1.$ a binary tree

$T=V,EV$: the set $of$ nodes, $E$: the set $of$ edges

$is$ defined recursively $as$ follows:

$a$ a single node $is$ a binary tree

$b$ given two binary trees $T_L$and $T_R,$ a tree $T$ whose root has $T_L$and $T_R$as its left and right children is also a binary tree.

for any binary tree T $=($V$,$E$)$ prove that $|$V$|=|$E$|+1$

$($show base case, inductive hypothesis, and inductive step.$)$