$($a$)$ Construct a DFA that does not recognise L $(\backslash$Sigma $=\{$a$,$ b$\}),[5$ marks$]$

where L $=\{$w$|$w ends with abb$\}.$

$($b$)$ Show that regular languages are closed under union, intersection and comple$-[8$ marks$]$

ment.