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(See Solution) Let L = (01 +11 +011)* and let M = 011*01 . Write down all strings in L whose length is less than 6. Prove that L properly contains M (i.e.,

Question: Let L = (01 +11 +011)* and let M = 011*01 .

  1. Write down all strings in L whose length is less than 6.
  2. Prove that L properly contains M (i.e., M \(\subseteq \) L but M \(\ne \) L).
  3. Let A = {00, 11, 10} and B = {1, 00, 10} . Find a string of length 2 which is in A* ∩ B* but not in (A ∩B )*.

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