UGC NET CSE | October 2022 | Part 1 | Question: 4

Question

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?

• A. Statement $\text{I}$ is true and Statement II is false
• B. Statement $\text{II}$ is true and Statement $\mathrm{I}$ is false
• C. Both Statement $\text{I}$ and Statement $II$ are true
• D. Neither Statement $\text{I}$ nor Statement $\text{II}$ is true

Comments

CFL are not closed under three operation

set difference ,complimentation ,intersection

and closed under all operation  

so statement first is correct and second is wrong

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Option C should be correct. Please check again

Answer 1

CFL is not closed under complement, intersection and difference operation. it is closed under homomorphism operation.

so statement I is true and II is false. Option (A) is correct.

REF:Closure Property of Language Families