Page 219 - DCAP402_DCAO204_DATABASE MANAGEMENT SYSTEM_MANAGING DATABASE

Database Management Systems/Managing Database

Notes Let us define certain equivalence rules that may be used to generate equivalent relational
expressions.

Equivalence Rules

1. The conjunctive selection operations can be equated to a sequence of individual selections.
It can be represented as:

2. The selection operations are commutative, that is,

3. Only the last of the sequence of projection operations is needed, the others can be omitted.

4. The selection operations can be combined with Cartesian products and theta join operations.

5. The theta-join operations and natural joins are commutative.

6. The Natural join operations are associative. Theta joins are also associative but with the
proper distribution of joining condition:

7. The selection operation distributes over the theta join operation, under conditions when
all the attributes in selection predicate involve only the attributes of one of the expressions
(E1) being joined.

8. The projections operation distributes over the theta join operation with only those
attributes, which are present in that relation.

9. The set operations of union and intersection are commutative. But set difference is not
commutative.

10. Set union and intersection operations are also associative.

11. The selection operation can be distributed over the union, intersection, and set-differences
operations.

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