Final answer:
It is false that leaf nodes appear in the same relative order for preorder, inorder, and postorder traversals. Preorder, inorder, and postorder traversals visit nodes in different orders, especially affecting the sequence of leaf nodes.
Step-by-step explanation:
The statement that when you print out the nodes of a binary tree, the leaf nodes appear in the same relative order for the preorder, inorder, and postorder traversals is False.
For clarification, the leaf nodes are the nodes of a binary tree without any children. In preorder traversal, a node is processed before its children, in inorder traversal, a node is processed between its children, and in postorder traversal, a node is processed after its children. The relative order in which leaf nodes would appear would be different for each type of traversal. Specifically, in an inorder traversal, the leaf nodes are visited in ascending order based on their keys, as this traversal results in a sorted order for binary search trees.
If we notice that the leaf values increase in order, from right to left, for leaves shown to the left of the stem, while the leaf values increase in order from left to right, for leaves shown to the right of the stem, it does not mean that this pattern will apply to other traversals; instead, this observation can generally be attributed to the inherent properties of the binary search tree and does not hold true for the leaf node order across different traversal methods.