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Here is a transition table for a DFA$:$

- Give all the regular expressions $R_{ij}^{0}.$ Note$:$Think of state $q_{i}$ as if it were the state with integer number $i.$
- Give all the regular expressions $R_{ij}^{1}.$ Try to simplify the expressions as much as possible.
- Give all the regular expressions $R_{ij}^{2}.$ Try to simplify the expressions as much as possible.
- Give a regular expression for the language of the automaton.
- Construct the transition diagram for the DFA and give a regular expression for its language by eliminating state $q_{2}.$

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