Which of the following is false ?

Answer summary: Two statements in the list are false; the question as written is ambiguous because it asks for a single false statement.

• Statement: "Every binary relation is never be in BCNF." — This is false. Many binary relations are in BCNF. For a relation with two attributes A and B, if there are no non‑trivial functional dependencies (neither A->B nor B->A holds), then the pair {A,B} is the key and the relation satisfies BCNF. A binary relation can violate BCNF in special cases (for example if an attribute is constant so the empty set determines it), but that does not make the universal "never" claim true.

• Statement: "Every BCNF relation is in 3NF." — This is true. BCNF is a stronger condition than Third Normal Form; any relation meeting BCNF constraints will also meet 3NF requirements.

• Statement: "1 NF, 2 NF, 3 NF and BCNF are based on functional dependencies." — This is misleading/false. 2NF, 3NF and BCNF are defined using functional dependencies. First Normal Form (1NF) is instead concerned with atomicity of attribute values and the elimination of repeating groups; it is not defined in terms of functional dependencies.

• Statement: "Multivalued Dependency (MVD) is a special case of Join Dependency (JD)." — This is true. An MVD can be expressed as a particular join dependency that decomposes the relation into projections on the attribute sets involved in the MVD.

Conclusion: The statements about binary relations and about 1NF are both false. The question should be revised to avoid ambiguity (for example, ask "Which statements are false?" or correct the inaccurate statement about normal forms).