Explain following in context of Relational algebra: 1. Selection 2. Theta(θ) – Join 3. Projection.

Explain following in context of Relational algebra:  1. Selection   2. Theta(θ) – Join  3. Projection.

1. SELECTION (σ)

The SELECT operation is used for selecting a subset of the tuples according to a given selection condition. Sigma(σ) Symbol denotes it. It is used as an expression to choose tuples which meet the selection condition. Select operator selects tuples that satisfy a given predicate.

Notation: σp(r)

Where 

σ stands for selection predicate,

r stands for relation,

p is prepositional logic formula, 

which may use connectors like AND, OR and NOT,

These terms may use relational operators like: =, ≠, ≥, < ,  >,  ≤.

Example 1: σ topic = "Database" (Tutorials)

Output : Selects tuples from Tutorials where topic = 'Database'.

Example 2: σ topic = "Database" and author = "ABC"( Tutorials)

Output: Selects tuples from Tutorials where the topic is 'Database' and 'author' is ABC.

Example 3: σ sales > 50000 (Customers)

Output:  Selects tuples from Customers where sales is greater than 50000


2. Theta (θ) Join

Theta join combines tuples from different relations provided they satisfy the theta condition. The join condition is denoted by the symbol θ.

Notation: R1 θ R2

R1 and R2 are relations having attributes (A1, A2, .., An) and (B1, B2,.. ,Bn) such that the attributes don’t have anything in common, that is R1 ∩ R2 = Φ.

Theta join can use all kinds of comparison operators.

Consider the following table

Table 1 : Student

SID Name Std

101 Siya  10

102 Riya  11


Table 2 : Subjects

Class Subject

10 Math

10 English

11 Music

11 Sports

       

Example: STUDENT Student.Std = Subject.Class SUBJECT

Output:

Student_detail

SID Name Std Class    Subject

101 Siya         10 10    Math

101 Siya         10 10    English

102 Riya         11 11    Music

102 Riya         11 11    Sports


3. Projection(π)

The projection eliminates all attributes of the input relation but those mentioned in the projection list. The projection method defines a relation that contains a vertical subset of Relation.

This helps to extract the values of specified attributes to eliminates duplicate values. (pi) symbol is used to choose attributes from a relation. This operator helps you to keep specific columns from a relation and discards the other columns.

Notation:  ∏A1, A2, An(r)

Where A1, A2 , An are attribute names of relation r.

Duplicate rows are automatically eliminated, as relation is a set


Consider the following table

Table : Customer

Customer ID Customer Name   Status

1                 Google           Active

2                 Amazon           Active

3                 Apple           Inactive

4                 Alibaba                Active


Example: Π CustomerName, Status (Customers)

Output:

Customer Name  Status

Google                 Active

Amazon                 Active

Apple                 Inactive

Alibaba                 Active