Discussion
Which of the following is correct statement ?
(i) A language is a regular language if and only if it can be represented by a regular expression.
(ii) A language is a regular if and only if it cannot be generated by a regular grammar.
(iii) Every regular grammar is context free grammar.
Answer: C
Statements (i) and (iii) are correct, so the answer is (i) and (iii) only.
Statement (i) is Kleene's theorem: a language is regular if and only if some regular expression describes it. Statement (iii) is true because a regular grammar's productions (a variable going to a terminal string optionally followed by one variable) are a special case of context-free productions, so every regular grammar is context-free.
Statement (ii) is false: a language is regular if and only if it can be generated by a regular grammar. Options that include (ii), or that leave out (i), are wrong.
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