Let pk(R) denotes primary key of relation R. A many-to-one relationship that exists between two relations R1 and R2 can be expressed as follows :
pk(R1) → pk(R2)
A relationship between two entity sets can be written as a functional dependency between their primary keys (Silberschatz). In a many-to-one relationship from R1 to R2, many tuples of R1 may be associated with the same tuple of R2, but each tuple of R1 is associated with at most one tuple of R2.
Since a given R1 tuple determines exactly one associated R2 tuple, the primary key of R1 functionally determines the primary key of R2: pk(R1) → pk(R2). This is also why, when the relationship is mapped to tables, the primary key of R2 is placed as a foreign key on the many side, R1.
pk(R2) → pk(R1) describes the opposite direction, a many-to-one relationship from R2 to R1. The dependencies whose right side is R1 ∩ R2 describe the common attributes of the two schemas, which is the lossless-join condition for a decomposition, not a mapping cardinality between the relations.
pk(R1) → pk(R2) option is correct.
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