Consider the productions A $$ \to $$ PQ and A $$ \to $$ XY. Each of the five non-terminals A, P, Q, X, and Y has two attributes: s is a synthesized attribute, and i is an inherited attribute. Consider the following rules.

Rule 1 : P.i = A.i + 2, Q.i = P.i + A.i, and A.s = P.s + Q.s
Rule 2 : X.i = A.i + Y.s and Y.i = X.s + A.i

Which one of the following is TRUE?

Consider the augmented grammar given below :

S' → S
S → 〈L〉 | id
L → L,S | S

Let I₀ = CLOSURE ({[S' → ●S]}). The number of items in the set GOTO (I₀ , 〈 ) is: _____.

Consider the following parse tree for the expression $$a \ne b\$ c\$ d \ne e \ne f,$$ involving two binary operators $$\$ $$ and $$ \ne $$.

Which one of the following is correct for the given parse tree?

A student wrote two context-free grammars G1 and G2 for generating a single $$C$$-like array declaration. The dimension of the array is at least one. For example, $$${\mathop{\rm int}} \,\,\,\,\,\,\,a[10]\,\,[3];$$$

The grammars use D as the start symbol, and use six terminal symbols int ; id [ ] num.

Grammar G1	Grammar G2
D → intL;	D → intL;
L → id[E	L → idE
E → num	E → E[num]
E → num][E	E → [num]

Which of the grammars correctly generate the declaration mentioned above?