tHeorem 6.21: Let H be a subgroup of G. H .is a normal subgroup of g iff ghgEH for yg∈ G and h∈H Example:LetG={(X;y川x,y∈ R with x≠0}, and consider the binary operation o introduced by (x, y)o(z,w)=(xz, xw+) for (x,y),(z,w)∈G. Let H=l(, y yER. Is H a normal subgroup of g? Why? ◆1. H is a subgroup of c ◆2. normal? Theorem 6.21: Let H be a subgroup of G. H is a normal subgroup of G iff g-1hgH for gG and hH.  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 normal subgroup of G? Why?  1. H is a subgroup of G  2. normal?