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3 votes
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Consider the following languages:

  1. The language of regular expression $(0+1)^{\ast} 11(0+1)^{\ast}$
  2. The language of regular expression $\left(0^{\ast} 1^{\ast} 11\right)^{\ast} 0^{\ast} 110^{\ast} 1^{\ast}$

Which of the following is true?

  1. $1$ is a proper subset of $2$
  2. $2$ is the proper subset of $1$
  3. $1=2$
  4. Neither $1$ is a subset of $2$, nor $2$ is a subset of $1.$
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$1$ contains $2.\; 1$ is all strings of $0's$ and $1's$ with two consecutive $1's.\; 2$ misses some of these strings, e.g., something ending with $110101 .$
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