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# Introduction of Relations and Functions

#### 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.

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Relations and Functions part 1 (Concepts) [00:13:49]
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