- Relational Algebra Operators
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- Operators and Symbols
- Selection Operator
- Projection Operator
- Cartesian Product Operator
- Natural Join Operator
- Theta Join Operator
- Left Outer Join Operator
- Right Outer Join Operator
- Full Outer Join Operator
- Division Operator
- SET Union Operator
- SET Difference Operator
- SET Intersection Operator
- Rename Operator
Armstrong's Axioms Rules
FD1 - Reflexivity Rule
If Y Í X, then X ® Y
FD2 - Augmentation Rule
If Z Í W and X ® Y, then XW ® YZ
FD3 - Transitivity Rule
If X ® Y and Y ® Z, then X ® Z
There are three additional rules that are implied by the above rules.
FD4 - Pseudotransitivity Rule
If X ® Y and YW ® Z, then XW ® Z
FD5 - Union Rule
If X ® Y and X ® Z, then X ® YZ
FD6 - Decomposition Rule
If X ® YZ, then X ® Y and X ® Z
The rules of union and decomposition imply that we can always replace a set of functional dependencies with an equivalent set that has only functional dependencies of the form X ® A (i.e., the right-hand side contains a single attribute).
FD1 - Reflexivity Rule
If Y Í X, then X ® Y
FD2 - Augmentation Rule
If Z Í W and X ® Y, then XW ® YZ
FD3 - Transitivity Rule
If X ® Y and Y ® Z, then X ® Z
There are three additional rules that are implied by the above rules.
FD4 - Pseudotransitivity Rule
If X ® Y and YW ® Z, then XW ® Z
FD5 - Union Rule
If X ® Y and X ® Z, then X ® YZ
FD6 - Decomposition Rule
If X ® YZ, then X ® Y and X ® Z
The rules of union and decomposition imply that we can always replace a set of functional dependencies with an equivalent set that has only functional dependencies of the form X ® A (i.e., the right-hand side contains a single attribute).
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