Q$1$ :$(1\mathrm{.}1)$ Given the following language $\backslash ($ L$=\backslash \{$a b $\backslash ),$ aa $,$ baa $\backslash (\backslash \}\backslash ),$ Which of the following strings are in L$*.$

$1.$ abaabaaabaa

$(1$ mark$)$

$2.$ aaaabaaaa

$3.$ baaaaabaaaab

$4.$ baaaaabaa

Q$2$:$(2\mathrm{.}1)$ Write the regular expression for the language $\backslash ($ L $\backslash )$ over $\backslash (\backslash$Sigma$=\backslash \{0,1\backslash \}\backslash )$ in which every $0$ is immediately followed by $11.$

$(1$ mark$)$

Q$3$:$(2\mathrm{.}2)$: $3\mathrm{.}1$ Design a Turing machine that accepts the language $01*0.(2$ marks$)$