Given the following grammar:

X $->$ Y a

$|$ Z b

where X$,$ Y$,$ and Z are non$-$terminals and a and b are terminal symbols. We don't know the details of Y and Z$,$ but assume that they themselves can be parsed by an LL$(1)$ parser and are not mutually recursive with X$.$

Select all correct statements

Question $2$Select one or more:

$1.$Depending on what Y and Z look like, the grammar for X might have a common left factor.

$2.$The grammar for X can be parsed by an LL$(1)$ parser no matter what Y and Z look like.

$3.$ No matter what Y and Z look like, the grammar for X cannot be ambiguous.