Select all the statements below which are TRUE: If G is a context-free grammar,

Question

Select all the statements below which are TRUE: If G is a context-free grammar, then the left-most derivation is obtained if the left-most variable is replaced at each step of the derivation. Let G = (V. T, S. P) be a context-free grammar. Then a partial derivation tree of G can have the root labeled different than S. Consider the grammar below: S rightarrow AaAa | Bb A rightarrow Aaa |lambda B rightarrow b After removing the lambda - production, we get the following equivalent grammar: S rightarrow AaAa | aAa | Aaa | Bb A rightarrow Aaa | aa B rightarrow b The grammar below is an s-grammar: S rightarrow aS | bA A rightarrow aA | bB | a B rightarrow b If L is a context-free language, then L is regular. Let G be a context-free grammar. If a string w elementof L(G) is the yield of two different derivation trees of G. then G is ambiguous.

Explanation / Answer

Statement 1 --> It is true, as a leftmost derivation is obtained by applying production to the leftmost variable in each of the steps.

Statement 2 --> It is true.

Statement 3 --> it is true, as by removing the null productions in given NFA we recieve the provided one.

Statement 4 --> It is true, it is a simple grammar because it contains only a single terminator in each step e.g. S-> aBACDVD is a Simple Grammar

Statement 5 --> It is false, as regular language is not a proper subset of Context Free Language

Statement 6 --> It is true

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