$($a$)$ Construct a DFA that recognizes the following language, $\backslash$Sigma $=\{$a$,$ b$\}[5$ marks$]$

L $=\{$w$|$w does not end with bba$\}$

$($b$)$ Convert the each of the following regular expressions into an NFA. $[8$ marks$]$

$($a $\backslash$cup b $\backslash$cup c$)$

$000$

$((($ab$)$

$$

$(01))\backslash$cup a$)$

$$

$($c$)$ Construct a DFA that L$1\backslash$cap L$2.$ In all parts $\backslash$Sigma $=\{0,1\}.[7$ marks$]$

$1.$ L$1=\{$w$|$w contains even number of $0$s$\}$

$2.$ L$2=\{$w$|$w contains odd number of $1$s$\}$

$($d$)$ Use the pumping lemma to show the following language is not regular $[5$ marks$]$

$\{0$

n$1$

n

$|$n in N$\}$