Question 7965 – GATE 2017 [Set-2]

Since CFL is closed under UNION so L₁ ∪ L₂ is CFL, is a true statement.
CFL is not closed under complementation.
So L₁ compliment may or may not be CFL. Hence is Context free, is a false statement.
L₁ – R means and Regular language is closed under compliment, so
is also a regular language, so we have now L₁ ∩ R .
Regular language is closed with intersection with any language, i.e. L∩R is same type as L.
So L₁∩R is context free.
CFL is not closed under INTERSECTION, so L₁ ∩ L₂ may or may not be CFL and hence IV^th is false.