Question

For the grammar G given below, which of the strings are in L(G)

S -> aA I λ
A -> bS
I. λ
II. a
III. b
IV. aa
V. ba
VI. ab
VII. bb
a). IV
b). VI
c). III
d). VII
e). V
f). II
g). I

Answer 1

Only strings III (b), V (ba), VI (ab), and I (lambda/empty string) are in the language L(G) described by the given grammar G.

Step-by-step explanation:

The student is asking which strings belong to the language generated by the grammar G with the following production rules:

• S -> aA
• S -> λ (lambda represents the empty string/epsilon)
• A -> bS
• A -> λ

Let's analyze the given strings:

• II. a: Does not comply with the rules of G, as there is no rule that produces a single 'a' without it being followed by A.
• III. b: Produced by the rule A -> bS followed by S -> λ.
• IV. aa: Produced by the rule S -> aA followed by A -> a, which is not defined in G, therefore not in L(G).
• V. ba: Produced by the rule S -> aA, followed by A -> bS and then S -> λ.
• VI. ab: Produced by the rule S -> aA followed by A -> bS and then S -> λ.
• VII. bb: Produced by the rule S -> aA, followed by A -> bS and then S -> aA, which does not match as there is no a after the second b.
• I. λ: Produced directly by S -> λ.

Summarizing, the strings in L(G) from the options given are:

• III. b
• V. ba
• VI. ab
• I. λ