3. [5 points]

(a) Draw two non-isomorphic binary trees T and T' each with 11 vertices with

the property that every vertex is either a terminal vertex (with no children,

also known as a leaf) or has exactly 2 children.

(b) How many leaves does T have? How many leaves does T' have?

(c) Let T" be a tree with 101 vertices with the property that every vertex is a

leaf, or has exactly two children. Make a guess as to the number of leaves

in T". [Hint: consider the Handshake Theorem]

(d) Prove the guess you made in part (c).

(e) Is there a tree with 100 vertices such that every vertex is either a leaf or has

exactly two children? Justify your answer.