Define a context-free-grammar that has only strings in L (G) are a^n b^n for n ≥ 1.

Define a context-free-grammar that has only strings in L (G) are aⁿ bⁿ for n ≥ 1.

We can represent a CFG (G) by its four components that is
G = (V, T, P, S)
Where,
V = The set of variables
T = The set of terminals
P = The set of production
S = The start symbol
Here,
V = {s}
T = {a, b} and
P consists of the following rules.
{1. S → asb & 2. s → ab}
Whenever rule 1 is applied one ‘a’ is generate generate on the left and one ‘b’ the right. The derivation terminals by using rule 2. A simple derivation and derivation tree one given below:
S → asb
→ aasbb
→ aaasbbb
→ aaaasbbbb
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A simple derivation tree