# Predicitve Parser LL(1) condition

Lets say we use the predictive parser LL(1). Why is it necessary that

$$FIRST(\alpha) \cap FIRST(\beta) = \emptyset$$,

for all $$\alpha, \beta$$ right side of alternative productions i.e., productions associated to the same non-terminal. Why is this condition necessary?

If the right hand side of a production $$\alpha$$, $$\beta$$ have intersecting FIRST sets, then we'd have multiple rules at a single entry in the LL(1) table (i.e. duplicate/conflicting entries) --- having nontrivial intersection of FIRST sets essentially prevents us from constructing the LL(1) parsing table.