For two distinct productions A → α | β of a grammar G, the grammar is LL(1) if…

Concept: In an LL(1) grammar, one lookahead symbol must select exactly one production. Therefore the predictive sets of two alternatives for the same nonterminal must be disjoint.

For A → α | β, shared terminal symbols cause a parsing-table conflict. Both alternatives also cannot derive ε; if either alternative derives ε, the other alternative’s FIRST set must be disjoint from FOLLOW(A).

Application:

• The terminal-disjointness condition prevents FIRST(α) and FIRST(β) from sharing a terminal symbol.

• The ε-exclusion condition prevents α and β from both deriving ε.

• The nullable-alternative condition requires FIRST(α) ∩ FOLLOW(A) = ∅ when ε ∈ FIRST(β), and symmetrically FIRST(β) ∩ FOLLOW(A) = ∅ when ε ∈ FIRST(α).

Cross-check: If a terminal appeared in both FIRST sets, or if a nullable alternative overlapped FOLLOW(A), the LL(1) table would place two productions in one cell. The three conditions prevent those conflicts.

Result: Terminal disjointness, exclusion of shared ε, and the nullable-alternative FOLLOW condition are all required.