multiple choice: An appropriate grammar for the palindromes over the alphabet {a

Question

multiple choice:

An appropriate grammar for the palindromes over the alphabet {a, b, c} is:

a) S aSa | bSb | cSc | a | b | c

b) S aSa | bSb | cSc | a | b | c |

c) S aSa | bSb | cSc |

d) S aSb | bSc | cSa | a | b | c |

Please explain with answer, thank you.

a) S aSa | bSb | cSc | a | b | c

b) S aSa | bSb | cSc | a | b | c |

c) S aSa | bSb | cSc |

d) S aSb | bSc | cSa | a | b | c |

Explanation / Answer

b) S aSa | bSb | cSc | a | b | c | S aSa | bSb | cSc This will generate palindrome strings over alphabet a, b and c S -> a | b | c This will leave a letter a or b or c in the middle S -> This will not leave any letter in middle, making it an even letter palindrome. So, answer is b.

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