Number Theory

(2) (5 points) Let G be a group. In class we defined a subgroup of G to be a nonempty subset H satisfying: . For any h, h' E H, we also have hh' E H. . For any h EH, hale H. Show that a subset H C G is a subgroup (in the sense defined above) if and only if it is a group when equipped with the group operation coming from GI