Construct DFAs that recognize the following languages, and draw the diagram for each automaton $($you do not need to provide the tuples$).$ Justify why your DFAs are correct. Your justifications need not be formal proofs, but should explain clearly and specifically why what you$$ve drawn accepts all and only those strings in the given

language. For all constructions in this class $($starting now with DFAs and NFAs, and continuing later to PDAs and Turing Machines$),$ you should justify why your constructions are correct.

Let $=\{0,1\}.$Draw a DFA containing no more than $5$ states that recognizes L $=\{$w $$ w does not contain $0011\}.$