$($a$)$ If L$1$ L$2$ and L$1$ is non$-$regular, then L$2$ is non$-$regular. $($b$)$ If L$1$ L$2$ and L$2$ is non$-$regular, then L$1$ is non$-$regular. $($c$)$ If L is non$-$regular, then L$$ is non$-$regular. $($d$)$ If L$1$ and L$2$ are non$-$regular, then L$1$ L$2$ is non$-$regular. $($e$)$ If L$1$ and L$2$ are non$-$regular, then L$1$ L$2$ is non$-$regular