Please answer True or False on the following:

1. Let L = { w ^* | w = w^R }, where = {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 L^3 ? (that is, is w an element of the language L L L?)

2. Let L = { w ^* | w = w^R }, where = {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 = . Is w L^3 ? (that is, is w an element of the language L L L?)

3. Let L = { w ^* | w = w^R }, where = {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 L^3 ? (that is, is w an element of the language L L L?)

4. Let L = { w ^* | w = w^R }, where = {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 L^3 ? (that is, is w an element of the language L L L?)

5. Let L = { w ^* | w = w^R }, where = {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 L^3 ? (that is, is w an element of the language L L L?)