Consider an implementation of binary trees with Scheme lists, as in the following example:

Before proceeding, it may be useful to define three auxiliary functions (val T), (left T) and (right T), which return the value in the root of tree T, its left subtree and its right subtree, respectively.

(a) Write a recursive function (tree-member? V T), which determines whether V apppears as an element in the tree T. The following example illustrates the use of this function:

> (tree-member? 17 T)

#t

(b) Write a recursive function (preorder T), which returns the list of all elements in the tree T corresponding to a preorder traversal of the tree. The following exapmle illustrates the use of this function:

>(preorder T)

(13 5 1 8 9 22 17 25)

(c) Write a recursive function (inorder T), which returns the list of all elements in the tree T corresponding to a inorder traversal of the tree. The following example illustrates the use of this function:

>(inorder T)

(1 5 8 9 13 17 22 25)

de fineT'135 100) 80900))(221700 250022)) de fineT'135 100) 80900))(221700 250022))