which one is true in a group Please offer me a hint  for determining if the following statements are true or false.

a) If $H$ and $K$ ar normal and solvable in $G$ then $HK$ is normal and solvable.
b) If $H$ and $K$ are normal and abelian subgroups in $G$, then $HK$ is normal and abelian.

Thank you very much.

Hopefully you have no trouble showing that $HK$ has to be normal, if $H$ and $K$ are.
Hint for a): Use the fact that for $N\lhd G$, $G$ is solvable iff $G/N$ and $N$ are solvable, and look at the group $HK/H$ through the eyes of an isomorphism theorem.
Hint for b): the only concern is that elements of $H$ might not commute with elements of $K$. Try to find an example where this does not occur. 
