Final answer:
In an ordered tree, it is theoretically possible for in-order to match pre-order traversal, and post-order to be reverse pre-order in very specific structures. However, in a proper binary tree, in-order cannot match pre-order, nor can post-order be reverse pre-order due to the fixed traversal patterns.
Step-by-step explanation:
The question whether it is possible for an ordered tree's in-order traversal to visit nodes in the same order as pre-order traversal, and vice versa with post-order traversal, depends on the tree structure. In the case of a general ordered tree, it is theoretically possible for in-order and pre-order traversals to visit nodes in the same order if the tree is structured in a particular manner. For instance, consider a tree where every node has only right children, the in-order and pre-order traversal would visit the nodes in the same sequence because there are no left children to create a difference in order. However, for post-order traversal to visit nodes in reverse pre-order, the tree will have to be structured so that every node only has a left child, which would again result in the described visitation order, but this is a very contrived example and is not general.
When the tree is a proper binary tree, the in-order traversal cannot match the pre-order traversal order because in-order traversal will always visit the left subtree, then the root, and then the right subtree, whereas pre-order traversal visits the root, then the left subtree, followed by the right subtree. As for post-order traversal in a proper binary tree, the nodes will be visited in left subtree, right subtree, and then the root, which cannot produce a reverse pre-order traversal order. In both in-order vs pre-order and post-order in reverse pre-order comparisons for proper binary trees, it is impossible for the orders to be the same due to the fixed left-root-right (in-order) and root-left-right (pre-order) visiting patterns.