Suppose that we have two alphabets, $=\{$a$,$ b$,$ c$)$ and $22=\{0,1\},$ and we have a function f: $212,$ where f$($a$)=$ f$($b$)=0$ and f$($c$)=1.$ That is$.$ f maps a and b to O and c to $1.$ Now suppose that we extend f to F: $$ in the natural way: F$($w$)=$ F$($w$$w$...$ wn$)=$ f$($w$)$f$($w$)...$ f$($wn$).$ That is$,$ F maps a string symbol by symbols using f$.$ Syllabus For example, F$($aabbca$)=$ f$($a$)$ f$($a$)$f$($b$)$ f$($b$)$f$($c$)$f$($a$)=000010.$ Is it true that if language L is regular, then so is F$($L$)=\{$F$($w$)$: w in L$\}?$