Final answer:
None of the statements provided is valid for establishing a transitive relationship in the context of functional and multivalued dependencies within relational databases. Understanding the difference between functional and multivalued dependencies is crucial for maintaining data consistency and integrity in database theory.
Step-by-step explanation:
The question pertains to the transitive dependencies in a relational database, which involves the concept of functional dependencies, denoted as A->B (A functionally determines B), and multivalued dependencies, denoted as A->->B (A multivalued determines B). In the context of the question, it is important to understand the differences between these dependencies to identify the valid statement.
Statement (a) If A->->B, B->->C hold in relation R, then A->->C holds too implies a transitive multivalued dependency, which is not a valid inference in general. Statement (b) If A->->B, B->C hold in relation R, then A->->C holds too implies that if A multivalued determines B, and B functionally determines C, then A functionally determines C. This is also incorrect because multivalued dependencies do not guarantee functional dependencies. Statement (c) If A->B, B->->C hold in relation R, then A->->C holds too, implies that a functional dependency from A to B and a multivalued dependency from B to C lead to a multivalued dependency from A to C. This does not generally hold in database theory.
Each of these statements involves conditional and universal statements, important concepts in logic. We can use these logical concepts to analyze the relationships between entities and their attributes within databases, ensuring data consistency and integrity.
For understanding the truth of logical statements, one must recognize the difference between different kinds of dependencies. A functional dependency (A->B) means that if two tuples (rows) of a relation have the same value for attribute A, then they must have the same value for attribute B. A multivalued dependency (A->->B) allows tuples to have different values for attribute B, even if they have the same value for attribute A, provided that certain constraints are met.
Since no given option correctly reflects a valid transitive relationship involving multivalued dependencies, none of the provided statements is valid.