Saturday, March 30, 2013

45-List of Formulas - 03 Grade 11 and 12 Sets Relations and Functions-01

Blog-45

I delivered the lecture on Mathematical Fun.  It was delivered in Indian Language “Marathi”. If you understand Marathi, Please click here to see my Lecture on YouTube.

Secondly to think more about the studies of Mathematics, So you are requested kindly to allow your child to participate in Program of Studies for Students and Parents given in my previous Blog. (Blog-11)

1) Please tell your child to read the blog on "Simple Method of Multiplicationto learn something new concept of Multiplication.

Dear Students,

2) As per the request from so many students, the result of the question asked in BLOG-22 under the heading "Draw Perpendicular Bisector on Line Segment Drawn at the bottom of the page"  will be published on 02/04/2013. Till then you can also try to find the solution send me your procedure.

Today we will see the list of Formula (Formulae) of Set Relations and functions (Part-02).

Click on the link "List of Formulas - 02 Grade 11 and 12 Sets Relations and Functions" to see the previous Blog about the list of formulas on Sets Relations and Functions.


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:


Relation:
                  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.

Range:
                  Set of all the elements of Co-Domain B associated with the elements of Domain A is called the Range of Relation R.

Function:
                  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. 

Range:
                  Set of all the elements of Co-Domain B associated with the elements of Domain A is  called as the Range of Function f.

 Onto Function:
                 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).

Into Function:
                 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).

Even Function:
                 f : A -> B is said to be Even  Function if f (-x) = f (x).
                 Example: f (x) = cos x    
                 Example: f (x) = x2

Odd Function:
                 f : A -> B is said to be Even  Function if f (-x) = - f (x).
                 Example: f (x) = sin x    
                 Example: f (x) = x3
Composite Function: 


              If f: A ->; B, g : B-> C, then gof : A -> C where gof (x) = g[f(x)]
Inverse Function:
              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.

Anil Satpute