Problem 2 Binomial Tree Variant [4+4+6+6=20 marks] In the class, we learned that a binomial tree of order i can be formed by taking two copies of a binomial tree of order i - 1 and letting the root of one tree have the other tree as its first child. Consider the following definition of Fibomial trees: A Fibomial tree of order 0 is a single node and a Fibomial tree of order 1 is also a single node. A Fibomial tree of order i is formed by taking a Fibomial tree of orderi 1 and a Fibomial tree of order i - 2 letting the root of the first tree (of orderi-1) have the other tree as its first child (see the figure below i-2 Figure 1: Forming a Fibomial tree of order i from two Fibomial trees of ordersi 1 and a) Draw a Fibomial tree of order i = 5. b) Indicate whether the following statement is correct or not. Provide a justification f your answer. Let T denote the Fibomial tree of order k. The children of the root of T are the Fibonnial trees Tk-2. Tk-3, ,T, T, TO, To (more precisely, there is exactly one copy of each T, fori E (k- 2, k-3,..., 1) and two copies of To as a children of T). Problem 2 Binomial Tree Variant [4+4+6+6=20 marks] In the class, we learned that a binomial tree of order i can be formed by taking two copies of a binomial tree of order i - 1 and letting the root of one tree have the other tree as its first child. Consider the following definition of Fibomial trees: A Fibomial tree of order 0 is a single node and a Fibomial tree of order 1 is also a single node. A Fibomial tree of order i is formed by taking a Fibomial tree of orderi 1 and a Fibomial tree of order i - 2 letting the root of the first tree (of orderi-1) have the other tree as its first child (see the figure below i-2 Figure 1: Forming a Fibomial tree of order i from two Fibomial trees of ordersi 1 and a) Draw a Fibomial tree of order i = 5. b) Indicate whether the following statement is correct or not. Provide a justification f your answer. Let T denote the Fibomial tree of order k. The children of the root of T are the Fibonnial trees Tk-2. Tk-3, ,T, T, TO, To (more precisely, there is exactly one copy of each T, fori E (k- 2, k-3,..., 1) and two copies of To as a children of T)