(15%) For each of the relations R described below, describe in words the transitive closure R+ of R. (a) RY IFF X,Y E N and y = x+1 (b) RY IFF X, y are states of the US with a common land border. (Use actual geographic facts to give a concrete description of R+.) (c) xRY IFF X, y are adjacent vertices of an undirected graph. (15%) For each of the relations R described below, describe in words the transitive closure R+ of R. (a) RY IFF X,Y E N and y = x+1 (b) RY IFF X, y are states of the US with a common land border. (Use actual geographic facts to give a concrete description of R+.) (c) xRY IFF X, y are adjacent vertices of an undirected graph