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L1 = {a^nb^n, n>=0}

L2 = {a^nb^m , n not equal to m)

So how L1 U L2 is regular?


I know, L1 U L2 will have RegEx a*b* which is regular but how this RegEx comes can someone please take strings generated by L1 and L2 and then UNION them, I need to know how to UNION them strings. Thanks

asked in Theory of Computation by Loyal (4.6k points) 4 39 112 | 39 views

1 Answer

+3 votes
Best answer

A language is a set.

So, $L_{1} = \{a^{n}b^{n} : n \geq 0\}$

Which can be written like this: $\{\epsilon , ab, aabb, aaabbb, aaaabbbb, ... \}$.

And $L_{2} = \{a^{n}b^{m} : n \neq m\}$ 

Which is: $\{aab, abb, aaab, aaabb, abbb, aabbb, ... \}$.

When you union these two languages (or, sets), you get another set, which contains elements (or strings), which is in at least one of the two sets.

From this you can see, the union of these two languages will give:

$\{\epsilon , ab, aabb, aaabbb, aaaabbbb, ... , aab, abb, aaab, aaabb, abbb, aabbb, ... \}$

Which is nothing but the set of strings of the type $a^{*}b^{*}$.

Which is a regular language.

Hope it helps :)

answered by Loyal (3.6k points) 2 6 17
selected by

@Rishabh Gupta 2 Yes, it very much does! Thanks a lot.

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