Functional Dependancy

FUNCTIONAL DEPENDENCY (FD)

It is an attribute or a set of attribute that determines or implies the values of one or more attribute in the relation. It’s an association between two or more attributes in a relation or table.

For example: A -> B where A is determinant attribute and B is determined attribute. Here, we can see that there is an association between A and B in a table.

(C, A) -> B for composite attribute C and A

FULLY FUNCTIONAL DEPENDENCY (FFD)

The ‘determined’ attribute cannot be determined by any sub-set of the ‘determinant’ attribute.

For example: (C, A) → then A ↛ B

PRIMARY FUNCTIONAL DEPENDENCY (PFD)

A FD in which the ‘determinant’ attribute are the (primary) key attribute and the ‘determined’ attribute are non-key attribute is called PDF.

For example: B ⟶ A where B is primary key.

TRANSITIVE FUNCTIONAL DEPENDENCY (TDF)

A FD which may not directly exist in the relation but can be inferred from the FDs that exist in the same relation is referred to as TDF.

For example: A ⟶ B and B ⟶ C then A ⟶ C

DEPENDENCY DIAGRAM:

It’s a way of representing FD with a diagram.

It is a pictorial representation which indicates that which attribute in the relation determines other attribute in the relation.

For example: A⟶ B, C⟶D, A⟶F, B⟶C

example 2:

WELL FORMED FORMULA (WFF)

Every query is translated into WFF; if successfully translated then the formula is applied on the data and the result set is generated.

HOW TO DETERMINE WHETHER THE QUERY IS WFF OR NOT?

• Every condition is a well formed formula.
• A WFF is constructed from conditions, Boolean operators (&&, !, ||) and quantifiers like ( for all,  there exist).
• If F is a WFF them F’ (NOT F) is also a WFF.
• If F₁ and F₂ are two WFF then ‘F₁ and F₂’,’F₁ or F₂’ are also WFF.
• If F is a WFF in which t occurs as a free variable then t (F), t (F) are also WFF.
• Nothing else is WFF.

A general expression of the tuple relational calculus is of the form:

F = {t₁.A₁, t₂.A₂, …….. , t_n.A_n\ condition (t₁,t₂,t₃,….. , t_n)}

Where t₁, t₂, …. , t_n are tuple variables. Each A_i (i.e. A₁, A₂, A₃, ….) is an attribute of the relation on which ti ranges and conditions is the formula of the tuple relational calculus.