I need help with the following question on rooted trees. Please use structural induction to prove the statements. A perfect binary tree is one where every non-leaf node has two children, and all the leaf nodes are at the same level. Consider T to be a perfect binary tree of height h with n nodes: (a) Prove by induction that T has (n+1)/2 leaves. (b) Prove by induction that n = 2h+1 − 1.

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