0 votes 0 votes Suppose that we know that $L_1 ∪ L_2$ and $L_1$ are regular. Can we conclude from this that $L_2$ is regular? Theory of Computation peter-linz peter-linz-edition4 theory-of-computation regular-language closure-property + – Naveen Kumar 3 asked Apr 12, 2019 Naveen Kumar 3 378 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes If L1 U L2 is regular and L1 is regular, then we cannot conclude that L2 is also regular. Let L1 U L2= ∑* and L1 = ∑* Then L2 ={ aⁿbⁿ |n>=0} is not regular and L1 U L2 is regular. SuvasishDutta answered Apr 12, 2019 SuvasishDutta comment Share Follow See all 0 reply Please log in or register to add a comment.
0 votes 0 votes if L1 is regular and L1 U L2 is regular then we cannot conclude that L2 is regular , L1=(a+b)* , L2={a^n b^n |n>0} L1 U L2 = (a+b)* Sanandan answered Oct 3, 2020 Sanandan comment Share Follow See all 0 reply Please log in or register to add a comment.