* (a) Show that this language is not regular by applying the pumping
lemma directly.
(b) Then show the same thing by using the closure properties of regular
languages.
* 11. Show that the language
is not regular.
12. Apply the pumping lemma directly to show the result in Example 4.12.
13. Show that the following language is not regular.
14. Prove or disprove the following statement: If L 1 and L 2 are non regular
languages, then L 1 ∪ L 2 is also non regular.
15. Consider the languages below. For each, make a conjecture whether or not it
is regular. Then prove your conjecture.
16. Is the following language regular?
17. Let L 1 and L 2 be regular languages. Is the language L = {w : w ∈ L 1 , w R ∈
L 2 necessarily regular?
lemma directly.
(b) Then show the same thing by using the closure properties of regular
languages.
* 11. Show that the language
is not regular.
12. Apply the pumping lemma directly to show the result in Example 4.12.
13. Show that the following language is not regular.
14. Prove or disprove the following statement: If L 1 and L 2 are non regular
languages, then L 1 ∪ L 2 is also non regular.
15. Consider the languages below. For each, make a conjecture whether or not it
is regular. Then prove your conjecture.
16. Is the following language regular?
17. Let L 1 and L 2 be regular languages. Is the language L = {w : w ∈ L 1 , w R ∈
L 2 necessarily regular?