Properties of Regular Language

Question

Union of Regular and non Regular is?

Comments

Take $A = \Sigma^*$. Now you should get answer.

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I got it that B may be or may not be regular. e.g Let $A = a^*b^*$ and $B =  a^nb^n$  then $A \cup B = a^*b^*$ but consider $A=ab$ and $B = a^nb^n$ then $A \cup B =a^nb^n$ which is not regular.

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yes, thats all..

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thanks alot :)

Answer 1

B may be or may not be regular. e.g Let $A=a^∗b^∗ and B=a^nb^n then A\cupB=a^∗b^∗$ but consider $A=ab and B = a^nb^n then A \cup B = a^nb^n$ which is not regular.