S1 : true S2 : false
Explanation for S1:
On applying transitions look ahead does not get changed. Look ahead gets changed only applying on closure on the production.
Explanation for S2:
The lookahead shall have no effect in an item of the form [A → α.β, a] where β is not ∈.
[A → α.β, a] -> (applying transition on Beta ) -> [A → αβ., a] (look ahead remains same because First(a) = a )
[A → α., a] -> (applying transition) -> No Transition Possible because already reaches to reduction (look ahead remains same because First(a) = a )