You need to show a complete proof/ example for each item (e.g. DFA? RE, CFG/ PDA, Turing machine, DEC, P). If a DFA or a PDA exists, you still need to exhibit a Turing Machine recognizing the language. If it does not exist, a counterexample is required.

Let = {a, b}. Give a DFA/ RE, CFG/ PDA, and a turing machine that decides the language

L = { w|w contains exactly three a's or atleast one b},

if it exists. If any of the three does not exist, prove in detail why it does not exist. Is L P? (Justify your answers.)