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Answer
Step-by-step explanation
Why not in 1NF?
A table is in 1 NF iff:
- There are only Single Valued Attributes.
- Attribute Domain does not change.
- There is a Unique name for every Attribute/Column.
This table is not in 1NF because it has an attribute that is not single valued. It has several values for each cell in the column telNos.
Why not in 2NF?
A table is in the second normal form if it fulfills the following two requirements:
- It is in first normal form.
- It does not have any non-prime attribute that is functionally dependent on any proper subset of any candidate key of the relation. A non-prime attribute of a relation is an attribute that is not a part of any candidate key of the relation.
In this case, the candidate key is staffNo, branchNo since you can derive all the other attributes from these attributes.
We can see here that
branchAddress is functionally dependent on branchNo, a subset of the candidate key. Since branchAddress is a non-prime attribute, this violates the 2nd condition of being in 2NF. Hence, this table is not in 2NF.
Why not in 3NF?
A table is in 3NF if and only if for each of its functional dependencies
X →
A, at least one of the following conditions holds:
- X contains A (that is, A is a subset of X, meaning X → A is trivial functional dependency),
- X is a superkey,
- every element of A \ X, the set difference between A and X, is a prime attribute (i.e., each attribute in A \ X is contained in some candidate key).
In this table, the candidate key is branchNo since we can derive all the other attributes from this attribute alone. We can also see that
name is functionally dependent on mgrStaffNo. Since mgrStaffNo does not contain name (Rule 1), mgrStaffNo is not a superkey (Rule 2), and the set difference of mgrStaffNo and name is not a prime attribute (Rule 3), this table is not in 3NF.
Reference:
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