Question

Consider grammar G with productions A → a | Aa | bAA | AAb | AbA

Choose a false statement :

1. aaabb is in L(G)
2. abb is in L(G)
3. A is start symbol of G
4. aaaabb is in L(G)

Answer 1

Correct Answer - Option 2 : abb is in L(G)

Concept:

A grammar G is formally defined as a tuple (N, ∑, P, S ). Such formal grammar is often called a rewriting system.

N  → Nonterminal symbol 

∑  → terminal symbol 

P → Production rules

S  →start symbol

Explanation:

Productions of G: A → a | Aa | bAA | AAb | AbA

N → {A}

P → { A → a | Aa | bAA | AAb | AbA}

∑ → {a, b}

S → {A}

Option 1: TRUE

A → AAb → AAAbb → aaabb

aaabb is in L(G)

Option 2: FALSE

A → AAb → Aab →aab

Therefore abb is not in L(G)

but abb is in L(G)

Option3: TRUE

A is start symbol of G

Option3: TRUE

A → AAb → AAAbb → AAAabb → AAaabb 

→ Aaaabb → aaaabb

Therefore aaaabb is in L(G)