Let L$1$ be a regular language and L$2$ be any language $($not necessarily regular$)$ over the

same alphabet $\backslash$Sigma $.$ Prove that the language L $=\{$x in $\backslash$Sigma $|$ x $$ y in L$1$ for some y in L$2\}$ is

regular. Do this by mathematically defining a DFA for L starting from a DFA for L$1$ and

the language L$2.$