GATE CS 2025 Set 2 Q41 — Parsing (LL, LR)

Consider two grammars $G_{1}$ and $G_{2}$ with the production rules given below: 

$G_{1} : S \rightarrow$ $if$ $E$ $then$ $S$ $|$ $if$ $E$ $then$ $S$ $else$ $S$ $|$ $a$

        $E \rightarrow b$

$G_{2} :S \rightarrow$ $if$ $E$ $then$ $S$ $|$ $M$ 

        $M \rightarrow$ $if$ $E$ $then$ $M$ $else$ $S$ $|$ $c$

        $E \rightarrow b$ 
 

where $if, then, else, a, b, c$  are the terminals. 

Which of the following option(s) is/are CORRECT?