Let T be rooted binary tree with n nodes, and let k be the positive integer. Recall that a subtree includes a vertex and all of its descendants.

(a) Describe that the pair M = (S,I) isn't a matroid, where S is the set of all vertices of T , and I is the family of vertex sets of all subtrees with at most k vertices.

(b) Discuss that the pair M = (S,I) is the matroid, where S is the set of all vertices of T , and I is the family of vertex sets that contain at most half of the vertices from every subtree.