Discrete math question (entry-level). Please read the problem carefully and answer only if you are sure you got the right answer. And please provide some explanation to your answers (doesn't need to be much). On the bottom is a general template of what the proof should look like.

Rough template:

Consider the following definition of a binary tree Bases Step: Nil is a Tree Recursive Step: If L is a Tree and R is a Tree and x E Z, then Tree(x, L, R) is a Tree We define the set of values stored in a binary tree as follows values(Nil) values(Tree(x, L, R))) values(L) U{x} Uvalues = We define the predicate BST on trees as follows BST(Nil)T BST(Tree(z, L, R))) BST(L) (Vy, y E values(L) y