CFL Language

Question

For A, B ⊆ Σ*, define
A/B = {x ∈ Σ* | ∃y ∈ B, xy ∈ A}
If L is a CFL and R is  regular, then L/R is

(A) Regular
(B) CFL but not regular
(C) Recursive but not CFL
(D) None of the above

Answer 1

B is correct CFL but not regular

Comments

Could you please elaborate it I am not getting how to solve this?

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solve this would be a proof by contradiction in which we assume that A is context free, B is regular, and then assume that A/B is not context-free. Since A is context free, we can construct an equivalent PDA that accepts A