21. Let G = (V, E) be an undirected graph. A vertex cover U is a vertex subset such that, any edge in E has at least one endpoint vertex in U.

(a) (2%). Let U be a vertex cover and M be a matching for G. Prove or disprove that, |M| ≤ |U|.

(b) (2%). Consider the following graph. Identify a maximum-size matching and a minimum-size vertex cover for it.