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

# TOC-grand test-Q2

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
+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

reshown Sep 8, 2019

+1 vote

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

Hence Option A

answered Sep 11, 2019 by (91,540 points)
answered Sep 8, 2019 by (4,530 points)