Question

Consider the following statements:
I. In a relation R, if some set of attributes X is such that closure set of X contains all the attributes of R i.e. X determines every attribute of R then X is a candidate key of R.

II. It is possible for a relation to have no non-trivial functional dependencies.

III. If set of all attributes combined from a candidate key for some relation R then R does not contain any non-trivial FD.

IV. In a relation R, If X is some set of attributes and Y is some prime attribute such that X determines Y is a non-trivial FD. Then R has at least two candidate keys.

Which of the above statements is/are false?

Answer 1

In statement I, in a relation R, if some set of attributes X is such that closure set of X contains all the attributes of R i.e X determines every attribute of R then x is a super key, not necessarily a candidate key of R. So, I is false .
Remaining all are true.