#Self Doubt

Question

Suppose L1 = CFL and L2 = Regular, We are to find out whether L1 – L2 = CFL or non CFL.

I have 2 approaches to this question and I am confused which is wrong:

1. L1 – L2 = L1 intersection L2’ 
   1. L2 being Regular L2’ is also Regular so CFL intersection Regular = CFL
   2. L2 being Regular L2’ is also Regular and every Regular Language is also CFL so CFL intersection CFL = non CFL.

Can somebody please clarify my doubt?

Comments

Thanks a lot Sir

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In the second case, we are talking about all those CFLs which are regular.

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@Vishal_kumar98 Thanks yes this would mean ultimately doing RL intersection CFL = CFL.