Final answer:
The statement is b. false; a balanced tree ensures node's child subtree heights differ by at most one, not that all leaves are at the same level.
Step-by-step explanation:
The statement that a rooted tree is balanced if and only if all of its leaves are at the same level is b. false.
In computer science, a balanced tree, such as an AVL tree or a red-black tree, is one where the heights of the two child subtrees of any node differ by no more than one.
This does not necessarily mean all leaves must be at the exact same level, but rather that the tree is structured in such a way that no leaf is much further from the root than any other, which helps ensure that operations such as insert, delete, and find can be performed efficiently.