Please do (a) and (b) and any of the remaining parts. This is related to recursion and induction. You may use 'base case', 'step case'. Thank you so much!

CExercise 123. Assume we have a function f:S +T. (a) Recursively define a function map f that takes a binary tree with labels from S to a binary tree with labels from T, that is map f: FB Treess + FBTreest. Hint: Consider the map function for lists as an example. (b) For the function f:N - N n + 2n apply the function map f you defined in part (a) step by step to the following tree. tree17(tree5 (tree 3, tree 19), tree25 (tree 19, tree 27)) (c) Show that for every such function f, and every tree t in the set FBTreess, we have hght((map f)t) = hght t. (d) Show that for every such function f and every tree t in the set FB Treess we have no((map f)t) = not. (e) Assume that N is a set of numbers between N and R. Show that for the function k: N + N n+1 we have for all binary trees t that not = sum((map k)t). CExercise 123. Assume we have a function f:S +T. (a) Recursively define a function map f that takes a binary tree with labels from S to a binary tree with labels from T, that is map f: FB Treess + FBTreest. Hint: Consider the map function for lists as an example. (b) For the function f:N - N n + 2n apply the function map f you defined in part (a) step by step to the following tree. tree17(tree5 (tree 3, tree 19), tree25 (tree 19, tree 27)) (c) Show that for every such function f, and every tree t in the set FBTreess, we have hght((map f)t) = hght t. (d) Show that for every such function f and every tree t in the set FB Treess we have no((map f)t) = not. (e) Assume that N is a set of numbers between N and R. Show that for the function k: N + N n+1 we have for all binary trees t that not = sum((map k)t)