The Basic Mathematics of SQL

Introduction

Formally, we know a relation is a subset of a Cartesian Products of sets. i.e $ R \in ( A X B ) $
For Example.
$$ A = \{ 1, 3 \} , B = \{ 2, 5 \} $$
Cartesian Product of set A and B will be
$$ P = \{ (1,2),(3,2),(1,5),(3,5)\} $$

Out of that there are three pair that observe the $ < $ relationship
$$ R = \{ (1,2), (1,5), (3,5)\} $$
Or we can 1 is related to 5 by relation R ($<$)

In real world we name each relation by name which makes sense for others,
and with each relation name we associate its schema - which is a sequence of
attributes(i.e a column in Table)

For Example for above set we have a relation of $ R (A,B) $ which we can write more as

• lessthan(A,B)
  In Real world we represent the relation in Table with attributes as column
• Student(Id, FirstN, LastN)

Note : Attributes names in relation schema must be different