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Let $L_1$ and $L_2$ be languages over $\Sigma$ and assume that $L_1 \cap L_2 = \phi$. if $L_1$ is finite language and $L_1 \cup L_2$ is regular then $L_2$ is ____ ?

a. Regular language and finite

b. Regular language and infinite

c. Need not be regular

d. None of these.

closed as a duplicate of: plz answer

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+1 vote
As L1 is regular and  L1⋃L2 is regular then L2 must be regular as RL are closed under Union. But we can't say whether L2 is finite or infinite bcz it may be or may not be finite... Correct me if I am wrong
by Active (3.3k points)
+2
not always

but in this case.