Please answer True or False on the following: 1. Consider the language L = a^n b

Question

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 a’s, where n >= 0, followed by (n+1) b’s. 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 a’s, where n >= 0, followed by (n+1) b’s. 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 a’s, where n >= 0, followed by (n+1) b’s. 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 a’s, where n >= 0, followed by (n+1) b’s. 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 a’s, where n >= 0, followed by (n+1) b’s. 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 a’s, where n >= 0, followed by (n+1) b’s. Let w = aabbbabb. Is w L^* ? (that is, is w an element of the Kleene closure of L?)

Explanation / Answer

Solution 1) TRUE
Reason:for n=0 , w= will come

Solution 2) FALSE
Reason: the length of 'a' and 'b' are never same like 'ab', Hence this is false

Solution 3) FALSE
Reason: 'b' cannot come before 'a', first n times 'a' come followed by n+1 times 'b' will come.

Solution 4) TRUE
Reason: for n=3, w=aaabbbb will come.

Solution 5) FALSE
Reason: first n times 'a' come followed by n+1 times 'b' will come.

Solution 6) FALSE
Reason: first n times 'a' come followed by n+1 times 'b' will come.

Explanation:

the strings generated with the given language L = an b(n+1), where n>=0 are:

when n=0, w=
when n=1, w=abb
when n=2, w=aabbb
when n=3, w=aaabbbb
when n=4, w=aaaabbbbb and so on..

Here, we see that the number of b's are always one more than the number of a's and also 'b' always follows 'a'.

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