Final answer:
Yes, every relation without transitive functional dependencies is in 2NF.
Step-by-step explanation:
2NF stands for Second Normal Form, which is a property of databases and relational databases. In 2NF, a relation should be in 1NF and should not have any partial dependencies. A relation is said to have a transitive functional dependency when a non-key attribute is determined by another non-key attribute through a different non-key attribute. So, the question is asking if every relation without transitive functional dependencies is in 2NF.
The answer is yes, every relation without transitive functional dependencies is in 2NF. This is because in 2NF, the only allowed functional dependencies are those that relate non-key attributes to the entire composite key. If there are no transitive functional dependencies, it means that every non-key attribute is directly dependent on the entire composite key, which satisfies the requirements of 2NF.
For example, let's say we have a relation R(A, B, C, D) with a composite key (A, B). If the relation has a functional dependency A -> B and B -> C, then there is a transitive functional dependency A -> C. But if there are no transitive dependencies, such as A determining C or B determining D, then the relation satisfies the requirements of 2NF.