[TOC]IIT-k Written test

Question

Consider a grammar $G$ with productions $P$. Let $INIT(G)$ be the grammar with production $P'$ such that

    $P' = P \cup ( A\rightarrow B \mid \text{such that } A->BC \text{ belongs to } P ) \cup ( A\rightarrow \epsilon \mid \text{such that} A\rightarrow b \text{ belongs to} P )$

    prove that:

a) Prefix(G) is subset of INIT(G)

b) INIT(G) is subset of Prefix(G)

Comments

@rahul sharma 5,What is INIT(G) and Prefix(G) here?

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INIT(G) is given in the question.

Prefix(G) contains set of all prefixes of all strings in the grammar(this is what i learnt in TOC). I have copied this question from interview experience.

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Okay. I just happened to overlook what's mentioned in the first line about INIT(G).