Gate2017 cs Q65

0. Consider the context-free grammars over the alphabet {a,b,c} given below. S and T are non-terminals
G₁: S → aSb|T,T → cT|∈
G₂: S → bSa|T,T → cT|∈
The language L(G₁)∩L(G₂) is

Answer
Comment
Array

Option : B
Explanation :
The Context free grammar given over alphabets ∑{a, b, c} with S and T as non terminals are:
G₁: S → aSb|T,T → cT|∈
G₂: S → bSa|T,T → cT|∈
Lets L(G₁) is the language for grammar G₁ and L(G₂) is the language for grammar G₂
L(G₁) = {aⁿc^mbⁿ|n,m ≥ 0}
L(G₂) = {bⁿc^maⁿ|n,m ≥ 0}
L(G₁) ∩ L(G₁) = {c^maⁿ|m ≥ 0}; which is infinite and regular

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