Let M $=($Q$,\backslash$Sigma $,$ q$0,\backslash$delta $,$ QF $)$ such that QF $=\{$qf $\}.$ Further, for

all $\backslash$sigma in $\backslash$Sigma $,\backslash$delta $($q$0,\backslash$sigma $)=\backslash$delta $($qf $,\backslash$sigma $).$ Suppose a string x $=\backslash$epsi is in L $=$ L$($M $).$ For any

k $>=1,$ define x$($k$)=$ x$.$x$....$ x$|\{$z $\}$

k times

$.$ Prove that for any k $>=1,$ x$($k$)$ in L$.$