9/12 2.6

Question 1

Theorem 2.6.1

Answer 1

The set of regular languages is closed under the union operation, i.e., if A1 and A2 are regular languages over the same alphabet Σ, then A1 ∪ A2 is also a regular language.

Question 2

Theorem 2.6.2

Answer 2

The set of regular languages is closed under the concatenation operation, i.e., if A1 and A2 are regular languages over the same alphabet Σ, then A1A2 is also a regular language

Question 3

Theorem 2.6.3

Answer 3

The set of regular languages is closed under the star operation, i.e., if A is a regular language, then A^∗ is also a regular language.

Question 4

Theorem 2.6.4

Answer 4

The set of regular languages is closed under the complement and intersection operations:
1. If A is a regular language over the alphabet Σ, then the complement ^–A = {w ∈ Σ^∗ : w /∈ A}
is also a regular language.

2. If A1 and A2 are regular languages over the same alphabet Σ, then the intersection
   A1 ∩ A2 = {w ∈ Σ^∗ : w ∈ A1 and w ∈ A2} is also a regular language.