I have some propositions regarding BSTs , please can someone confirm whether they are true or false:
1.Suppose we have a node $n_1$ with a value $val_1$ i.e $n_1(val_1)$
2.We wish to find the number of children of the predecessor node of $n_1$ , with respect to inline traversal (That is the number of children of node $n_2(val_2)$ with $val_2$ being the greatest number $val_2 < val_1$)
3.Assume for simplicity that the BST dosen't have any repetition
Proposition 1: Let $n_1$ have two children .Then $n_2$ has atmost one child i.e the number of children of $n_2$ can't be two
Proposition 2: Let $n_1$ have only one child and $n_1$ is not root ,then also $n_2$ has atmost one child.
Please ascertain whether these propositions are true , but if false can someone provide a counter example ?