The language generated by the below grammar is the set of ____________.S →→ aSa| bSb| a| b; a)all odd length palindromesb)all palindromesc)strings beginning and ending with the same symbold)all even length palindromes
Question
The language generated by the below grammar is the set of ____________.S →→ aSa| bSb| a| b; a)all odd length palindromesb)all palindromesc)strings beginning and ending with the same symbold)all even length palindromes
Solution
The language generated by the given grammar is the set of all strings beginning and ending with the same symbol.
Here's why:
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The grammar S → aSa | bSb | a | b generates strings that start and end with the same symbol.
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The first two productions aSa and bSb ensure that the string starts and ends with the same symbol.
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The last two productions a and b are the base cases, which are also strings that start and end with the same symbol.
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Therefore, any string generated by this grammar will start and end with the same symbol.
So, the correct answer is (c) strings beginning and ending with the same symbol.
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