Final answer:
A binary tree is not always a binary search tree. However, every binary search tree is a binary tree.
Step-by-step explanation:
a. Every binary tree is a binary search tree.
This statement is false. While every binary search tree is a binary tree, not every binary tree is a binary search tree. Binary search trees have a specific ordering property where the left child of a node is less than the node and the right child is greater than the node.
b. Every binary search tree is a tree.
This statement is true. A binary search tree is a type of tree that follows the binary tree structure.
c. Every binary search tree is a binary tree.
This statement is true. Every binary search tree is a binary tree because it follows the binary tree structure of having at most two children per node. The key difference is the ordering property of the binary search tree.