The Basic Relational Mathematics Behind 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)

| ID | FirstN | LastN | | — | :––: | —– |:| | 101 | John | Deo | | 102 | Jane | Deo | | 103 | Jhonny | Deo |

Note : Attributes names in relation schema must be different