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GO Classes DPP | COMPILER|FIRST SET

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Consider the following grammar $G$ with the set of non-terminals $\{S, A, B\}$ and terminals $\{a, b, c, d\}$ :

$$
S \rightarrow A B c, A \rightarrow a|\epsilon, B \rightarrow b| \epsilon
$$


Which of the following is the correct $\operatorname{FIRST}(\mathrm{S})$ ?

  1. $\{a, b, c, \epsilon\}$
     
  2. $\{a, b, c\}$
     
  3. $\{a, \epsilon\}$
     
  4. $\{a, b, \epsilon\}$

4 Answers

0 0 votes

Answer option B

Given grammar

S -> ABc
A -> a | €
B -> b | €

For the given grammar in the above question the First(S) can never contain €(epsilon) because the non terminal S cannot produce €(epsilon) by itself in the production of the given grammar. So, options A and C and D are eliminated.

now,first(s) =first(ABc)={ a , fi(B)(because fi(A) has null) }

Fi(b)= { b , c(because fi(b) has null)  }

Finally fi(S) = {a,b,c}

 

Anyone please correct me if my approach is wrong. 

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