Question

For each of the following claims, state whether it is True or False. Briefly explain your answer. (1) If Li and L2 are regular languages, then L1 L2 = {w:we (L1-L2) or w € (L2-L1)} is regular. (2) If Li and L2 are regular languages and L1 CL CL2, then L must be regular. (3) If Lis regular, then so is {xy : X E L andy & L}. (4) The union of a finite number of regular languages must be regular. (5) The union of an infinite number of regular languages must be regular.

Answer 1

1. True - compliment of two regular languages is always regular
2. True - a subset of L₂ is L and subset of L is L₁ so L will always be regular as its superset and subset contains regular language so L will also be regular
3. False - as x belongs to a regular language L, but y does not belong to L and L will not be able to produce y in their language
4. True - Every kind of finite set is regular if the  infinite union of finite language is always regular
5. False - it is not always the case for example aⁿ is regular bⁿ is regular but aⁿbⁿ { n = 0,1,2.....x} is not regular

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