$3.$ For each of the following give two strings that are members of the language, and two strings that are not members of the language. Assume the alphabet $\backslash$Sigma $=\{0,1\}.$

$1.\backslash$Sigma $00\backslash$Sigma $1\backslash$Sigma $.$

$2.(1\backslash$cup $10\backslash$cup $00)$

$3.(111)\mathrm{.}4.$ Give regular expressions generating the languages of Exercise $2.$ For $($a$),$ prove $($by induction$)$ that the language of your expression is equal to the language as described in $($a$).$