then l1 ∪ l2 is not regular

PDF	1 For each of the following statements indicate whether it is true or Let L1 is a regular language and L2 is a non−regular language and they are disjoint i e L1 ∩ L2 = ∅ Suppose L = L1 ∪ L2 and L is regular (since regular

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Definition: A language that cannot be defined by a regular expression is a nonregular language or an irregular language.

Can the union of 2 non-regular languages be regular?

O Yes, because of the closure property of regular languages under the union operation.
Yes, For instance, this is the case with the language constructed by the union of the two non-regular languages {a" b n = m} and {an bm n = m}, which is described by the regular expression a*b*.
O.

When l1l2 is regular and L1 is finite then L2 is regular?

(.
1) If L1 ∪ L2 is regular and L1 is finite, then L2 is regular.
TRUE.
Because L2 = (L1 ∪L2)−(L1 −L2).
The first part is regular by assumption, the second part is regular because it is finite (being a finite set minus something), and regular languages are closed under set difference.

There are subsets of a regular language which are not regular. 2. If L1 and L2 are nonregular, then L1 ∪ L2 must be nonregular. 3.Autres questions

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PDF	CS 341 Homework 9 Languages That Are and Are Not Regular (2) Every regular language except ∅ has a regular proper subset (j) If L1 and L2 are nonregular languages, then L1 ∪ L2 is also not regular False

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PDF	Additional Material Section 21 8 fév 2011 · If L1 is regular, L2 is not regular, and L1 ∩ L2 is regular, then L1 ∪ L2 is not regular 2 IT16 (2011) Chapter 2 11 / 17 Page 12 Exercise