Theorem 6.17: Let G; be a group, and h be a nonempty subset of G. Then H is a subgroup of G, iff a b-∈ H for va,b∈H Example: Let H, and H2: be subgroups of the group G;, Then H0H2; is also a subgroup of g;. IH1∪H2;] Example:eG={(x;y)xy∈ R with x≠0},and consider the binary operation o introduced by (x, y)o(zw)=(XZ, Xw +y for (x, y), (z W)EG. Let H=(, l yER) Is h a subgroup of g? Why?Theorem 6.17: Let [G;·] be a group, and H be a nonempty subset of G. Then H is a subgroup of G, iff a·b-1H for a,b H. Example: Let [H1 ;·] and [H2 ;·] be subgroups of the group [G;·] ， Then [H1∩H2 ;·] is also a subgroup of [G;·] [H1∪H2 ;·] ? Example:Let G ={ (x; y)| x,yR with x 0} , and consider the binary operation ● introduced by (x, y) ● (z,w) = (xz, xw + y) for (x, y), (z, w) G. Let H ={(1, y)| yR}. Is H a subgroup of G? Why?