GATE CSE 1989 | Question: 3-ii

Question

Context-free languages and regular languages are both closed under the operation (s) of :

• A. Union
• B. Intersection
• C. Concatenation
• D. Complementation

Comments

$\color{red}{\text{Find Detailed Video Solution Below}}$ $\color{BLACK}{\text{  , With Proof of each option:}}$

https://youtu.be/bz2b4XNjsWY

Answer 1

Answer: (A) and (C)

Regular language is closed under Union, Intersection, Concatenation, and Complementation.

CFL is closed under  Union Concatenation but not under Intersection or Complementation.

So, both closed under Union  Concatenation.

Comments

can you tell me example of " intersection of 2 regular language "??

Answer 2

CFL is not closed under Intersection, complementation and set difference.
 

Property	Regular language	CFL
Union	Closed	Closed
Intersection	Closed	No
Set Difference	Closed	No
Complementation	Closed	No
Intersection with a regular lang.	Closed	Closed
Concatenation	Closed	Closed

so Ans : Context-free languages and regular languages are both closed under Union and concatenation

Answer 3

Context-free languages and regular languages are both closed under the operation (s) of 
 

1. Union
2. Concatenation

Answer 4

Regular languages closed under Union, Intersection, Concatenation and Complementation but CFC is only closed under Union and Concatenation.
Hence both A and C