Problem $5(10$ points$)$ Let L be the set of strings that have the form ww where w is a string in $($a$\backslash$cup b$\backslash$cup c$)^(*).$

Let L$\_(1)$ be the language defined by the regular expression: a$^(*)$b$^(*)$c$^(*)$

Let L$\_(2)$ be the language defined by the regular expression: a$^(*)$b$^(*)$c$^(*)$a$^(*)$b$^(*)$c$^(*)$

$($a$)$ Let S$\_(1)=$L$\backslash$cap L$\_(1).$ Write a regular expression that defines S$\_(1).$ If such a regular expression does not exist, prove

it$.$

Answer:

$($b$)$ Let S$\_(2)=$L$\backslash$cap L$\_(2).$ Write a context free grammar that defines S$\_(2).$ If such a grammar does not exist, prove it$.$

Answer: