Write prolog clauses that define each of the following predicates: a. exactly_3(x) is true if x is a list with exactly three elements. b. at_least_3(x) is true if x is a list with at least three elements. c. at_most_3(x) is true if x is list with at most three elements. hint: use four clauses. d. intersect(x, y) is true if x and y are lists with an element in common. intersect([1,2,3,4],[5,4,1,6]) holds, but intersect([1,2,3,4],[5,6]) does not hold. hint: use member but no recursion. e. all_intersect(z, y) is true if every element of list z is a list x such that intersect(x, y) holds. all_intersect([[1,2,3],[5,4,6]],[3, 4]) holds, and all_intersect([],[3,4]) holds, but all_intersect([[1,2,3],[1,2,5],[5,4 ,6]],[3,4]) does not hold.