###### Question 7962 – GATE 2017 [Set-2]
November 16, 2023
###### Question 7968 – GATE 2017 [Set-2]
November 16, 2023
###### Question 7962 – GATE 2017 [Set-2]
November 16, 2023
###### Question 7968 – GATE 2017 [Set-2]
November 16, 2023

Let L1, L2 be any two context-free languages and R be any regular language. Then which of the following is/are CORRECT?

Correct Answer: B

Question 4 Explanation:
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 IVth is false.
I, II and IV only
I and III only
II and IV only
I only
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