Please help explain this solution. What does minimum size mean? What does maximum size mean? Also what is a decision problem?

Consider the following three definitions in a connected undirected graph G=(V, E): Minimum Vertex Cover (MVC) is a subset V' of V with min- imum size such that every edge (u, v) in E has at least one end in V'. Maximum Clique (MaxCliq) is a complete subgraph of G that has a maximum size. Maximum Independent Set (MIS) is a subset V' of V with maximum size such that for all u and v in V', edge (u, v) is not in E, called the independence property. - Explain how these problems relate with each other. - Write the decision problem of each one of the problems. Solution. If V' is a min vertex cover in G, then V - V' is a max independent set in G and V - V' is a max clique in the complement of G, denoted , where = (V, ) and contains all edges that do not exist in G. Decision problem of Minimum Verter Cover (MVC): INPUT: An undirected graph G = (V, E) and an integer k = |V. DECISION: Does G contain a vertex cover with size at most k? Decision problem of Maximum Clique (MaxCliq): INPUT: An undirected graph G = (V, E) and an integer k = |V. DECISION: Does G contain a clique with size at least k? Decision problem of Maximum Independent Set (MIS): INPUT: An undirected graph G = (V, E) and an integer k