Question

#1

We are given the grammar rules

A ➝ F B E

B ➝ A C

These rules are only some of the rules of a larger grammar G, but we are not given the remaining rules of G. We are told that A is the start symbol of G and that the following holds:

{ε, c, d} ⊆ FIRST(C)

{ε, e} ⊆ FIRST(E)

{ε, f, g} ⊆ FIRST(F)

Recall that end of file is denoted EOF. The symbol ⊆ is used to denote set inclusion. For example, {ε, c, d} ⊆ FIRST(C) means that ε, c, and d are all elements of FIRST(C). Which of the following must hold?

c ∈ FIRST(B)

EOF ∈ FIRST(B)

a ∈ FIRST(B)

ε ∈ FIRST(B)

f ∈ FIRST(B) -- Correct Answer

d ∈ FIRST(B)

Need explanation on how to get First(A) and First(B).

#2

We are given the grammar rules

A ➝ F E

B ➝ A C

           These rules are only some of the rules of a larger grammar G, but we are not given the remaining rules of G. We are told that A is the start symbol of G and that the following holds:

{ε, c, d} ⊆ FIRST(C)

{ε, e}      ⊆ FIRST(E)

{ε, f, g}   ⊆ FIRST(F)

Recall that end of file is denoted EOF. The symbol ⊆ is used to denote set inclusion. For example, {ε, c, d} ⊆ FIRST(C) means that ε, c, and d are all elements of FIRST(C). Which of the following must hold (more than one choice or no choice can be correct)?

ε ∈ FIRST(B) -- Correct Answer  

EOF ∈ FIRST(B)

f ∈ FIRST(B) --  Correct Answer  

d ∈ FIRST(B) --  Correct Answer  

c ∈ FIRST(B) --  Correct Answer  

I can get {f,g,e} for First(B). Need explanation why empty, d, and c are a part of First(B).

Answer 1