Question

Please answer True or False on the following:

1. Let L be a set of strings over the alphabet Σ = { a, b }. If L is infinite, then L* must be infinite (L* is the Kleene closure of L)

2. Let L be a set of strings over the alphabet Σ = { a, b }. Let ! L denote the complement of L. If L is finite, then ! L must be infinite.

3. Let L be a set of strings over the alphabet Σ = { a, b }. Let ! L denote the complement of L. If L is infinite, then ! L must be finite.

4. Let L be a set of strings over the alphabet Σ = { a, b }. If L is finite, then L* must be infinite.

Answer 1

1. Let L be a set of strings over the alphabet Σ = { a, b }. If L is infinite, then L* must be infinite (L* is the Kleene closure of L)false

2. Let L be a set of strings over the alphabet Σ = { a, b }. Let ! L denote the complement of L. If L is finite, then ! L must be infinite.true

3. Let L be a set of strings over the alphabet Σ = { a, b }. Let ! L denote the complement of L. If L is infinite, then ! L must be finite. true

4. Let L be a set of strings over the alphabet Σ = { a, b }. If L is finite, then L* must be infinite. false