Let H be a subgroup of group G. Let R = {Hg:g in G} be the collection of all right cosets of H in G and L = {gH: g in G} be the collection of all left cosets of H in G. Define phi: R --> L by phi(Hg) = g^-1H.
a) Show that phi is a well-defined mapping.
b) Prove that phi is one to one.
c) Prove that phi maps R onto L.