$(12$ marks$)$ Based on our discussion of strings and languages in class, list all of the strings in

each of the languages below. A first example is provided for you. See the bottom of the page for

some reminders of definitions, etc.

$$ L $=\{0$

m$1$

n

$|$ m$,$ n in Z

nonneg, m $+$ n $=5\}$

$$ Answer: L $=\{00000,00001,00011,00111,01111,11111\}$

$($a$)$ L$1=\{0$

m$1$

n $|$ m$,$ n in Z

nonneg, n $<=2,$ m $<=$ n$\}$

$($b$)$ L$2=\{$a

mb

n $|$ m$,$ n in Z

nonneg

$,2<=$ n $<=6,$ n is a multiple of m$\}$

$($c$)$ L$3=\{$a

nb

$2$n$1$c

$3$n$2$

$|$ n in Z

$+,$ n $<=3\}$

$($d$)$ L$4=\{$w in $\{$a$,$ b$\}$

$$

$||$w$|<=3$ and w is a palindrome$\}$

$($A palindrome is a string that is the same backwards and forwards, such as radar, racecar,

sees, abbababba and a$.)$