Mark the following statements as true or false.
a. A binary tree must be nonempty. $(1,2)$
b. The level of the root node is $0 .(1,2)$
c. If a tree has only one node, the height of the tree is 0 because the number of levels is 0 . (2)
d. The level of a node in a binary tree is the number of branches on the path from the root to the node. (2)
e. The inorder traversal of a binary tree always outputs the data in ascending order. (3)
f. In preorder traversal of a binary tree, the node is visited before visiting the left and right subtrees. (3)
g. In a binary search tree, the data in a node is larger than the data in its left child, if any. (5)
h. In a binary search tree, the left and right subtrees of a node are binary search trees. (5)
i. To insert a new item in a binary search tree, first we search the binary search tree and find the place where the new item is to be inserted. (7)