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Write regular expressions for the following languages$:$

  1. The set of all strings of $0's$ and $1's$ not containing $101$ as a substring.
  2. The set of all strings with an equal number of $0's$ and $1's,$ such that no prefix has two more $0'$ than $1's,$ nor two more $1's$ than  $0's.$
  3. The set of strings of $0's$ and $1's$ whose number of $0's$ is divisible by five and whose number of $1's$ is even.
in Theory of Computation by Veteran (59.1k points)
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