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Let A be a regular set. Consider the two sets below

L1={x | $\exists n\geq 0, \exists y\epsilon A :$ y=$x^n$}

L2={x | $\exists n\geq 0, \exists y\epsilon A :$ x=$y^n$}

which of the following statements is true?

  1. L1 and L2 both are regular
  2. L1 is regular but L2 is not
  3. L1 is not regular but L2 is
  4. L1 and L2 both are non-regular
in Theory of Computation by
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