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(Formal languages) Determine if the following statements are true or not: If L1 and L2 are...

(Formal languages)

Determine if the following statements are true or not:

If L1 and L2 are non-regular languages then is L1 intersection L2 non regular? (T/F)
If L1 is a non regular language and L2 is a finite language is it true that L1 union L2 is regular?
Is it true that the union of two regular languages must be regular?

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Homework Answers

Answer #1

1. Not True

Since if L1 and L2 are non-regular then their intersection should be regular because we can see the intersection of 2 non-regular languages is an empty set. So an empty set is a regular language.

2. True

We can say that union of a non-regular language and finite language is regular,

Σ∗∪ L2 = regular language where L2 is non-regular and the other is regular

It is also possible that the union of finite and non-regular is non-regular.

3.True

It is true that union of two regular language would always be regular ,

So there are certain theories which explains this such as according to formal theory and the theory of nondeterministic finite automata we can say that union of two regular language is regular.

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