Suppose we have a set of sports teams in a league L, and a set of games G among those teams. Each game has a home team and a visiting team, who are two different teams in the league. We have predicates H(g, t) meaning team t was the home team in game g and V(g, t) meaning team t was the visiting team in game g.

(a) Consider the predicate P(s, t) meaning team s played a game against team t. Can you express this predicate in terms of the predicates H and V, along with boolean operators? Either do it or explain (informally) why you cannot.

(b) If I have a list of the games played, and access to the H and V predicates, how could I compute the value of P(s, t) given two teams s and t?

(c) (uses Java) Assume that you have a Java class Game that includes instance methods boolean home(Team t) and boolean visitor (Team t). Write a static method boolean played(Team s, Team t, Game[ ] season) that will input two teams and an array of games, and return true if and only if P(s, t) is true for the set of games in the array.