Aspire Faculty ID #18802 · Topic: UGC NET Computer Science Sep 2022 (Paper II) · Just now
UGC NET Computer Science Sep 2022 (Paper II)

Consider the following statements about Context Free Language (CFL):

Statement I: CFL is closed under homomorphism.

Statement II: CFL is closed under complement.

Which of the following is correct?

Solution

Statement I:

Context Free Languages are closed under homomorphism.

It means if a language is context free, then its homomorphic image is also context free.

So, Statement I is true.

Statement II:

Context Free Languages are not closed under complement.

This means if $L$ is a CFL, then complement of $L$ may not be a CFL.

So, Statement II is false.

Therefore, Statement I is true and Statement II is false.

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