Fibonacci trees are defined as follows: - F1,F0 are a root consisting of a single node. - F1 is a root with exactly one child. - For i2,Fi is defined recursively as follows: Fi consist of a root with i children, where the jth child (1ji) is in turn the root of Fibonacci tree Fj2. (a) Draw F0,F4. (b) Prove that the Fibonacci tree Fi(i0) has fi+1 nodes, where fk is the the Fibonacci sequence. (The Fibonacci sequence is defined as f0=1,f1=1, fk=fk1+fk2,k2. Note that we use f0=1 here.)