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Consider the following statements about Context Free Language $\text{(CFL)}$ :
Statement I:  $\text{CFL}$ is closed under homomorphism.
Statement II: $\text{CFL}$ is closed under complement.

Which of the following is correct?

  1. Statement $\text{I}$ is true and Statement II is false
  2. Statement $\text{II}$ is true and Statement $\mathrm{I}$ is false
  3. Both Statement $\text{I}$ and Statement $II$ are true
  4. Neither Statement $\text{I}$ nor Statement $\text{II}$ is true
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