Let $G_{i}$ be a group with a normal subgroup $H_{i} \unlhd G_{i}$ for $i=1, 2$. Show that (a) $H_{1} \times H_{2} \unlhd G_{1} \times G_{2}$. (b) $\left(G_{1} \times G_{2} ight) Aleft(H_{1} \times H_{2} ight) \cong\left(G_{1} / H_{1} ight) \times\left(G_{2} / H_{2} ight) $. CS. SD. 129