Please answer True or False on the following:

1. Consider the language L = a^n b^(n+1). This languages consists of all strings over the alphabet = { a, b } consisting of some number n of as, where n >= 0, followed by (n+1) bs. Let w = . Is w L^* ? (that is, is w an element of the Kleene closure of L?)

2. Consider the language L = a^n b^(n+1). This languages consists of all strings over the alphabet = { a, b } consisting of some number n of as, where n >= 0, followed by (n+1) bs. Let w = ab. Is w L^* ? (that is, is w an element of the Kleene closure of L?)

3. Consider the language L = a^n b^(n+1). This languages consists of all strings over the alphabet = { a, b } consisting of some number n of as, where n >= 0, followed by (n+1) bs. Let w = baaba. Is w L^* ? (that is, is w an element of the Kleene closure of L?)

4. Consider the language L = a^n b^(n+1). This languages consists of all strings over the alphabet = { a, b } consisting of some number n of as, where n >= 0, followed by (n+1) bs. Let w = aaabbbb. Is w L^* ? (that is, is w an element of the Kleene closure of L?)

5. Consider the language L = a^n b^(n+1). This languages consists of all strings over the alphabet = { a, b } consisting of some number n of as, where n >= 0, followed by (n+1) bs. Let w = abbaabbbabb. Is w L^* ? (that is, is w an element of the Kleene closure of L?)

6. Consider the language L = a^n b^(n+1). This languages consists of all strings over the alphabet = { a, b } consisting of some number n of as, where n >= 0, followed by (n+1) bs. Let w = aabbbabb. Is w L^* ? (that is, is w an element of the Kleene closure of L?)