#### notes

In this chapter, we are going to discuss what is a relation and how do we find the domain, co-or domain and the range of the relation. Before we begin with what is a relation you need to have know what is a set, cartesian product, relation which would finally extended to a function.

A set is a well defined collection of objects, that means whichever way you take you get a unique answer.

Cartesian product is considered as `"A" xx "B"` which is defined to be all those ordered pairs where the first element comes from the first step and the second element comes from the second set and `xx` is referred as cross.

Example: A is a set having elements (1,2,3) and set B have elements (a,b,c,d).

`"A" xx "B"`= {(1,a), (1,b), (1,c), (1,d), (2,a), (2,b), (2,c), (2,d), (3,a), (3,b), (3,c), (3,d)} this is our entire cartesian product which moves from A to B. Once we have the knowledge of this let's extend this to a relation.

Relation is a connection between two sets A and B such that relation is a part or a subset of this cartesian product A cross B means here we have taken all possible ordered pairs from A to B whereas for a relation we'll be a little selective.

Example- Relation: all ordered pairs begining with an odd number

R= {(1,a), (1,b), (1,c), (1,d), (3,a), (3,b), (3,c), (3,d)},

That means relation is a part of a cartesian product.

R: A→B

R⊆ A X B

Example- A={1,2,3,4,5} B= {4,6,9}

R is a relation from A to B, R= {(x,y) difference between x and y is odd x∈A, y∈B}

R= {(1,4), (1,6), (2,9), (3,4), (3,6), (5,4), (5,6)}

Domain- Set of all the 1st elements in the ordered pairs of R

Domain= {1,2,3,5}

Range- 2nd elements in the ordered pairs of R

Range= {4,6,9}

Co-Domain- is the 2nd set i.e B.