$\backslash$Sigma $=\{$a$,$b$,$c$,$d$,$e$\}$ and S be the language $($aa$+$bb$+$cc$+$ddd$+$eee$)$ Prove that for all naturals n except for$=1$ n$=1,$ there exists a string of length n in S$.($Hint: Show the $=0$ n$=0$ case separately and then use induction for all n with$>=2$n$>=2.)$