Consider the Grammar, G, with the production rule: S-> aS | bS | ε Which of the following is generated by G? Options :{a n b m | m,n >=0}{w ∈ {a, b}*, w has equal number of a’s and b’s}{a, b}*{an |n >=0} ∪ {bn |n >=0} ∪ {anbn |n >=0}
Question
Consider the Grammar, G, with the production rule: S-> aS | bS | ε Which of the following is generated by G? Options :{a n b m | m,n >=0}{w ∈ {a, b}, w has equal number of a’s and b’s}{a, b}{an |n >=0} ∪ {bn |n >=0} ∪ {anbn |n >=0}
Solution
The grammar G generates the language {a, b}*. This is because the production rule S -> aS | bS | ε allows for the generation of any string of a's and b's, including the empty string ε.
Let's break it down:
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{a^n b^m | m,n >=0}: This language is generated by G. The grammar G can generate any number of a's followed by any number of b's, including zero.
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{w ∈ {a, b}*, w has equal number of a’s and b’s}: This language is not generated by G. The grammar G does not enforce any condition on the number of a's and b's being equal.
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{a, b}*: This language is generated by G. As mentioned earlier, the grammar G can generate any string of a's and b's, including the empty string.
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{a^n |n >=0} ∪ {b^n |n >=0} ∪ {a^n b^n |n >=0}: This language is also generated by G. The grammar G can generate any number of a's, any number of b's, and any number of a's followed by the same number of b's.
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