Theory of Automata concepts

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I just started taking Theory of Automata and I'm having a hard time understanding some of the concepts. It's been only a week and the following questions are my homework. I'm not asking you to do my homework for me but I was just hoping someone could solve with explanations the first part (a) of each question so I can do the rest myself. So far I can only understand how automata's work on state diagrams. Everything other than that seems confusing. Hope someone can explain.

Thanks again.

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