Question

Please answer True or False on the following:

1. Let L = { w ε Σ^* | w = w^R }, where Σ = {a, b}. In other words, L is the set of all palindromes (including the empty string). A palindrome is a string that reads the same from left-to-right as from right-to-left. Let w = aababbbabb. Is w ε L^* ? (that is, is w an element of the Kleene closure of L?)

2. Let L = { w ε Σ^* | w = w^R }, where Σ = {a, b}. In other words, L is the set of all palindromes (including the empty string). A palindrome is a string that reads the same from left-to-right as from right-to-left. Let w = λ. Is w ε L^* ? (that is, is w an element of the Kleene closure of L?)

3. Let L = { w ε Σ^* | w = w^R }, where Σ = {a, b}. In other words, L is the set of all palindromes (including the empty string). A palindrome is a string that reads the same from left-to-right as from right-to-left. Let w = ab. Is w ε L^* ? (that is, is w an element of the Kleene closure of L?)

4. Let L = { w ε Σ^* | w = w^R }, where Σ = {a, b}. In other words, L is the set of all palindromes (including the empty string). A palindrome is a string that reads the same from left-to-right as from right-to-left. Let w = aababaa. Is w ε L^* ? (that is, is w an element of the Kleene closure of L?)

5. Let L = { w ε Σ^* | w = w^R }, where Σ = {a, b}. In other words, L is the set of all palindromes (including the empty string). A palindrome is a string that reads the same from left-to-right as from right-to-left. Let w = ababbabbbaa. Is w ε L^* ? (that is, is w an element of the Kleene closure of L?)

Answer 1

1. Let L = { w ε Σ^* | w = w^R }, where Σ = {a, b}. In other words, L is the set of all palindromes (including the empty string). A palindrome is a string that reads the same from left-to-right as from right-to-left. Let w = aababbbabb. Is w ε L^* ? (that is, is w an element of the Kleene closure of L?)

-- >True

2. True

3. False

4. True

5. False