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Recognize the language

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If L be a language recognizable by a finite automata, then language from {L}={w such that w is prefix of v where v belongs to L},is a

a. Regular Language

b. Context Free language

c. Context Sensitive Language

d. Recursive Enumerable Language
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Prefix of a langauge are finite. Therefore, {L} will be regular language. Option (A)

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Take the DFA and convert all the states as accepting ones for accepting all prefixes.

If you want only the proper prefixes convert all the states to accepting ones, then exclude  the initial state and the final states, but then include the states that are one transition away from any other final state.
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