Regular Languages

Question

If L1 contains finite number of strings and L2 is a CFL then $L1\cap L2$ is ____

(A) Regular
(B) CSL
(C) CFL
(D) None of these

Answer 1

CFL is not closed under intersection and complementation . Given two CFLs you cant decide but regular intersection leads to CF

pg34 problem5

http://www.idt.mdh.se/kurser/dva337/compendia/context_free_languages.pdf 

Answer 2

It will be regular. Option A

Any finite language can be represented by a FA therefore its regular.

Since L1 is finite set

Say,S1={a3,a23,a7,a90,a5}

L2 be a CFL

Say,S2={a1,a2,a3,a4,...}

Now, S1 intersection S2

S={a3,a23,a7,a90,a5}

Which is again FINITE  and hence can be represenred by FA and hence Regular.

Therefore A is correct its REGULAR.