Let $\displaystyle A,B $ be two subgroups of $\displaystyle G$ where only $\displaystyle A$ is normal.

If $\displaystyle x \notin AB$, does it mean that $\displaystyle x \notin A$ and $\displaystyle x \notin B$?

Suppose $\displaystyle x \notin AB$ and $\displaystyle y \notin A$. Does it implies $\displaystyle xy \notin A$?