Answer the questions below for the sets of strings:

C $=\{\backslash$epsi $,$ aab, baa$\},$

D $=\{$bb$,$ aab$\},$

E $=\{\backslash$epsi $\},$

F $=.$

Except for parts $($c$)$ and $($h$),$ write out any sets with the elements in string order,

i$.$e$.,$ shorter strings appear before longer strings, and strings of the same length are in

alphabetical order. For any infinite sets, list only the first $8$ elements in string order,

but be sure to also indicate that the set is infinite by including $3$ dots after listing the

first $8$ elements. For any set S of strings, we define

S

$=\{$ x$1$x$2$ xk $|$ k $>=0$ and each xi in S $\},$

S

$+=\{$ x$1$x$2$ xk $|$ k $>=1$ and each xi in S $\},$

where the concatenation of k $=0$ strings is the empty string $\backslash$epsi $.$

$($a$)$ What is D $\backslash$cup C $?$

$($b$)$ What is C $\backslash$cup F $?$

$($c$)$ What is C $\backslash$times D $?$

$($d$)$ What is C $\backslash$cap D $?$

$($e$)$ What is D $$ C $?$

$($f$)$ What is C $$ E $?$

$($g$)$ What is D $$ D $$ D $?$

$($h$)$ What is P$($C$),$ the power set of C $?$

$($i$)$ What is D $$ C $?$

$($j$)$ What is C$+?$

$($k$)$ What is F

$$

$?$

$($l$)$ Is E $$ C $?$

$($m$)$ Is D $$ C $?$

$($n$)$ For this part, we first need some definition