Recall that a k-ary tree is a rooted tree where each node has up to k children (for some positive integer k).

(a) Write a recursive definition of a nonempty A-ary tree with height h greaterthanorequalto 0.

(b) A complete A-ary tree is a A-ary tree analogous to a complete binary subtree, except that each internal node has k children (not just 2), and all those children arc complete A-ary trees of equal height.

Write a conjecture about how many leaves are present in a nonempty complete A-ary tree of height h.

(c) Prove your conjecture using structural induction.