Final answer:
The traversal that outputs elements in sorted order in a binary search tree is the in-order traversal. It visits nodes starting from the left subtree, then the node itself, followed by the right subtree, resulting in a sorted sequence.
Step-by-step explanation:
Binary Search Tree Traversal
In a binary search tree (BST), the traversal that outputs the elements in sorted order is the in-order traversal. During an in-order traversal, the algorithm visits the nodes in the following order: it starts with the left subtree, then visits the node, and finally, the right subtree. This process results in the elements being output in ascending order. To illustrate, if a BST has nodes with values 3, 5, 7, 8, and 10, the in order traversal would output them as 3, 5, 7, 8, 10, which is sorted.
The other traversal options, such as Post order Option 2, Level order Option 3, and Preorder Option 4, do not guarantee a sorted output. Postorder traversal finishes with the root node, levelorder traversal moves across the tree level by level, and preorder traversal begins with the root node, none of which produce a sorted list inherently.