in Theory of Computation
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  1.   LC may be CFL
  2.   LC cannot be CFL
  3.   LC may be regular
  4.   LC may or may not be CFL
in Theory of Computation
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LA ->CFL

LB ->Regular

LA U LB ->CFL

CFL intersection LC -> CFL

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

Option (1) is wrong

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2 Answers

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1 vote
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.
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Option 1 is wrong

CFL is not closed under intersection complementation and subtraction.

So Lc can be regular

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