Question

Let G=(V, T, P, S) be a CFG such that _____________. Then there exists an equivalent grammar G’ having no e productions.

(a) e ∈ L(G)

(b) w ∉ L(G)

(c) e ∉ L(G)

(d) w ∈ L(G)

I got this question in class test.

Origin of the question is Eliminating Epsilon Productions in division Properties of Context Free Languages of Automata Theory

Answer 1

Correct answer is (c) e ∉ L(G)

For explanation I would say: Theorem: Let G = (V, T, S, P) be a CFG such that  e ∉ L(G). Then there exists an equivalent grammar G’ having no e-productions.