A) List of Important Blogs related to School/College Studies:
01) Number of elements in a set:
The Number of distinct elements in a finite set A is denoted by n (A).
02) Some Important Results:
Cartesian Product of two sets:
If A and B are any two non-empty sets, then any subset of A x B is called relation from A to B. If R is the relation from A to B and (x , y) belongs to R, then we say that xRy. Here Set A is the Domain, set B is the Co-Domain. Y is called as the image of x under relation R. Similarly, x is called the pre-image of y under relation R.
Set of all the elements of Co-Domain B associated with the elements of Domain A is called the Range of Relation R.
A and B are two non-empty sets. The Function f from A to B is said to be a function if every element of set A is associated with unique element of set B and is denoted as f : A -> B. and we say that y = f(x). Here y is the image of x under function f.
Here we say that, A is the Domain and B is Co-Domain.
Set of all the elements of Co-Domain B associated with the elements of Domain A is called as the Range of Function f.
f : A-> B is Onto function if every element of Co-Domain B is associated with some
elements of A under Function f. (Note: Range of f is same as Co-Domain).
f : A ->; B is Into function if there exits at least one element extra in Co-Domain B which is not associated with any element of Domain A under Function f. (Note: Range of f is not same as Co-Domain).
f : A -> B is said to be Even Function if f (-x) = f (x).
Example: f (x) = cos x
Example: f (x) = x2
f : A -> B is said to be Even Function if f (-x) = - f (x).
Example: f (x) = sin x
Example: f (x) = x3
If f: A ->; B, g : B-> C, then gof : A -> C where gof (x) = g[f(x)]
If f : A -> B is one-one onto Function, then g : B ->A is known as an inverse function of f and is denoted as f-1 : B -> A.