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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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TOC-grand test-Q2


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+1 vote

Consider the following statements

S1 : If A, \small A $\cup$ B, and \small A $\cap$ B are regular languages, then B is regular as well.

S2 : For any nonregular languages \small L_{1} \subseteq L_{2} \subseteq L_{3} \small $\subseteq$ ..... the union \small L=\bigcup_{n=1}^{\infty }L_{n} is non regular

Which of the above statements are TRUE ?

(A) Only S1

(B) Only S2

(C) Both S1 and S2

(D) Neither S1 or S2

asked Sep 7, 2019 by gbeditor-2 (72,840 points)
reshown Sep 8, 2019 by gbeditor-2

2 Answers

+1 vote
 
Best answer

S1 : True

One can obtain B from the regular languages A , A \cup B , A \cap B  using set difference: 

B = (A \cup B) - ( A - (A \cap B) )  Since regular languages are closed under set difference, B must be regular as well.

S2 : False

image

Hence Option A

 

answered Sep 11, 2019 by (91,540 points)
0 votes
answer is option A
answered Sep 8, 2019 by (4,530 points)
Answer:

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Warning: count(): Parameter must be an array or an object that implements Countable in /home/customer/www/thegatebook.in/public_html/qa/qa-include/qa-theme-base.php on line 177

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