Solution:If H is a non-empty finite subset of a group G such that ab∈H for all a , b∈H, then H is also a group under the operation of G restricted to H. This is because H inherits associatively, identity and inverses from G, and closure under the group operation is given. So the statement (1) is correct. There does exist a homomorphism form (Z, +) to (Q, +).
One such homomorphism is the identity map, Which maps every integer in Z to the corresponding rationed number in Q. This map preserves addition, making it a homomorphism.