For any n

$,$ define the language Bn$=\{$ak$$k is a multiple of n$\}$

over the alphabet $\{$a$,$b$\}$

$.$

Give a DFA for B$5$

$.$ Make sure your automaton has a transition from each state, labeled by each letter $($a

or b

$).$

Show that for all n

$,$ Bn

is regular by giving a DFA for it$.$ For full credit, you have to give a definition that depends on n

$,$ hence you cannot answer with a drawing, you have to specify the DFA Mn

with language Bn

as a $5-$tuple $($Qn$,\backslash$delta n$,\backslash$Sigma $,$q$0,$Fn$)$

$.$