Consider the following two sets of LR(1) items of an LR(1) grammar. $$\begin{array}{ll} X \rightarrow c.X, \text{ } c/d & X \rightarrow c.X, \text{ } \$ \\ X \rightarrow .cX, \text{ } c/d & X \rightarrow .cX, \text{ } \$ \\ X \rightarrow .d, \text{ } c/d & X \rightarrow .d, \text{ } \$ \end{array}$$ Which of the following statements related to merging of the two sets in the corresponding LALR parser is/are **FALSE**? 1. Cannot be merged since lookconjugates/lookaheads are different. 2. Can be merged but will result in S-R conflict. 3. Can be merged but will result in R-R conflict. 4. Cannot be merged since goto on $c$ will lead to two different sets.

In an LALR(1) parser, two sets of LR(1) items are merged if and only if they have the same core (i.e., identical productions with the dot in the exact same positions), regardless of their lookaheads.

Let us analyze each statement:

1. Statement 1 is FALSE: The two sets have identical cores ($X \rightarrow c.X$, $X \rightarrow .cX$, $X \rightarrow .d$). In LALR parser construction, states with the same core are merged by taking the union of their lookahead sets. Differences in lookaheads do not prevent merging.

2. Statement 2 is FALSE: None of the items in these sets are complete items ($A \rightarrow \alpha.$), so there are no reduce actions at all. Therefore, no Shift-Reduce (S-R) conflict can occur.

3. Statement 3 is FALSE: Since there are no reduce items in these sets, no Reduce-Reduce (R-R) conflict can arise.

4. Statement 4 is FALSE: For any transition (such as goto on $c$), the target states will also have identical cores and will correspondingly be merged into a single state in the LALR parser.

Since all statements 1, 2, 3, and 4 are false, the correct option is (D).