Math Relations

Let us learn about math relations,
Consider the two sets P = {a, b, c} and Q = {Ali, Bhanu, Binoy, Chandra, Divya}.
The cartesian product of
P and Q has 15 ordered pairs which
can be listed as P × Q = {(a, Ali),
(a,Bhanu), (a, Binoy), ..., (c, Divya)}.
We can now obtain a subset of
P × Q by introducing a relation R
between the first element x and the
second element y of each ordered pair
(x, y) as
R= { (x,y): x is the first letter of the name y, x ∈ P, y ∈ Q}.
Then R = {(a, Ali), (b, Bhanu), (b, Binoy), (c, Chandra)}
A visual representation of this relation R (called an arrow diagram) is shown
in Fig.
Definition 2 A relation R from a non-empty set A to a non-empty set B is a subset of
the cartesian product A × B. The subset is derived by describing a relationship between
the first element and the second element of the ordered pairs in A × B. The second
element is called the image of the first element.
Definition 3 The set of all first elements of the ordered pairs in a relation R from a set
A to a set B is called the domain of the relation R.
Definition 4 The set of all second elements in a relation R from a set A to a set B is
called the range of the relation R. The whole set B is called the codomain of the relation R. Note that range ⊆ codomain.
Hope the explanation helped you, now let me explain about math functions.