Let L be the set of all strings over $\{$a$,$b$\}$ that never have the same letter twice in succession. So$,$ the following are all in L: A$,$ a$,$ b$,$ ab$,$ ba$,$ aba, bab, abab, baba, etc.

Write a regular expression that generates L$.$

Draw a four$-$state DFA that recognizes L$.$

Either convert your DFA to a RE using the NFA$-$to$-$RE algorithm from class or convert your RE to an NFA using the RE$-$to$-$NFA algorithm from class, it's your choice which. Show enough work that it is clear to me that you are following the correct algorithm. Note: you might only get full credit for this step if the source DF$$ or RE is correct, so choose carefully