### Solvable Groups

If G is a finite group, define R = R(G) = INTERSECTION {K < G | G/K is solvable}. a. Show that R is the smallest normal subgroup of G, such that G/R is solvable. b. Show that G is solvable iff R = {1}. c. If H <= G is a subgroup, show that R(H) <= H INTERSECTION R(G). Please see the attachment for question with clear not