Relational Algebra/ Calculus

RELATIONAL ALGEBRA/ CALCULUS

It is a procedural language.

Traditional operations
UNION	INTERSECTION	DIFFERENCE	CARTESIAN PRODUCT
a U b or b U a	a ∩ b or b ∩ a	a-b or b-a	a˟b or b˟a

Set: It is a collection of elements.

e.g. A = {1,4,5,10,25} and B = {3,4,5} so, A˟B = {(1,3);(1,4);(1,5);(3,4);…….}

General Operator/ Operations:

• SELECTION: It’s the one that is applied on a relation and generates another relation which is a subset of relation on which the operation was applied. It is a horizontal operation.
• PROJECTION: when applied on a relation, returns a sub set of the original relation. It is a vertical operation.
• JOIN: equi-join -> when corresponding values are being searched in two tables with same value. The join is outer-join when only begins them value of set A which is in set B.
• DIVISION: two relation can only carry out division operation (assuming relation A having ‘m’ columns and relation B having ‘n’ columns) iff

(a) Relation B with n- columns can act as divisor n<m

(b) Relation B having n-columns must be a sub set of relation A

 The resultant set will again be a relation which will be a subset of relation A.

TUPLE

It is the foundation for records in a database. It is a set of variables which when placed together defines a relation.

Limitation of Relational Algebra:

• No recursion or iteration
• Cannot compute transitive closure.