For groups G and H, their direct product Gx H = {(g, h) | g G and h H} forms a group under the operation defined by (g, h)(g', h') = (gg', hh'), for all g, g G and h, h' H. (a) Show that every line N passing through the origin in R2 is a normal subgroup of G = (R, +). (b) For any such line N as in (a), describe G/N. (c) Show that G/N = R.