Regular and CFL

Question

1.   L_C may be CFL
2.   L_C cannot be CFL
3.   L_C may be regular
4.   L_C may or may not be CFL

Comments

L_A ->CFL

L_B ->Regular

L_A U L_B ->CFL

CFL intersection L_C -> CFL

As CFL is not closed under intersection, L_C is regular & not CFL

Option (1) is wrong

Answer 1

all options are correct except b) Lc cannot be CFL

All the closure properties are 1-way.

CFLs are not closed in intersection, it means that the intersection is not always a CFL, i.e., it may or may not be CFL.

Answer 2

Option 1 is wrong

CFL is not closed under intersection complementation and subtraction.

So Lc can be regular