After Eliminating the left recursion from the given grammar:

A → A*X / X
X → X+B / B
B → id 

Which of the following represent grammar to represent the equivalent left recursion free grammar?

(I): A → XA\'
A\' → *XA\'
X → BX\'
X\' → +BX\'
B → id

(II): A → XA\'
A\' → ϵ / *XA\'
X → BX\'
X\' → ϵ / +BX\'
B → id

(III): A → XA\' /ϵ
A\' → ϵ / *XA\'
X → BX\' /ϵ
X\' → ϵ / +BX\'
B → id

(IV): A → XA\' /ϵ
A\' → *XA\'
X → BX\' /ϵ
X\' → +BX\'
B → id 

(A) (I)
(B) (II)
(C) (III)
(D) (IV)


Answer: (B)

Explanation: Removal of left recursion:

A →  A x X / X will be results in 
  → X , X x X, X x X, X x X x X, ...X(x X)*
A → XA\'
A\'→ ϵ / x X A\'
X → X + B / B will be results in 
  → B , B + B, B + B + B, ...B(+ B)*
X → BX\'
X\'→ ϵ / +BX*
B → id  

So, option (B) is correct.

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