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CPT Chapter Sets Functions and Relations

CA CPT Exam  

With Anand.Duration:3hrs32min

Set ,Function, Relationship & Venn DiagramDuration (min:sec)
Set 
Overview & Index of Set03:47
What is Set08:34
How are Set Displayed10:28
Operations of Set11:48
Types of Set13:50
Compliment of Set04:38
Power of Set05:28
Union & Intersection04:42
Properties of Union & Intersection28:03
Set of Numbers06:01
Product Set04:11
Conclusion02:21
Functions & Relationship 
Index02:00
What is relationship & Function10:47
Solving Function11:21
Domain & Range07:46
Types of Functions09:38
Solving Types of Function19:14
Types of Relationship12:03
Venn Diagram08:15
Final Quiz26:46
Conclusion00:56
Total03:32:37

What is Set
How are Set displayed
Operations of Set
Types of Set
Complement of a Set
Power of Set
Union and Intersection
Set of Numbers
Product of Set

Set-
a collection of well defined distinct objects.
A={a,e,i,o,u}

Set: A is the (Capital Letter)

Element or Cardinal number :a,e,i,o,u (small letter)
examples:
B={1,3,5,7,9,11}
C={2,4,6,8,10,12}

How are sets displayed-

Roster form or Braces form

A={a,e,i,o,u}
B={1,3,5,7,9,11}
C={2,4,6,8,10,12}

Set Builder or Algebraic form

A= set of vowels in the alphabet
B=Odd number between 1 to 12
C=Even number between 1 to 12

Operations of Set-

A-B
Set of elements present in A but not in B.


AxB
Ordered pair of element in which the 1st element is from A and second from B, in each ordered pair.

Types of Set-

Universal Set - contains all element of all set under consideration
A{1,3,5} , B{2,4,6} , U{1,2,3,4,5,6}

Subset - If A has all the element of B , then B is subset of A
A={a,e,i,o,u}
B ={0,u}
B ⊂ A

If B is subset of A and A is not equal to B , then B is a proper subset of Q.

Singleton Set- with only one element
{1},{India}

Equal Set - every element of set A is in set B. order is not important.Repetition of element in a set is meaningless.
A {1,3,5} ,B {5,1,3} , A=B
A {1,3,5} ,B {5,1,3,1} , A=B
A {1,3,5} ,B {6,1,3} , A≠B

Disjoint Sets - Two sets have no element in common.
A {1,3,5} ,B {6,7,8} , A∩B = { }
Null Set : A set which has no element .
A{ } or A= Φ

Note : A= {Φ} is not null set instead it is a set which has Φ as its element.

Equal vs Equivalent Set-

Two sets which have same elements are Equal sets
Two sets have same number of elements are Equivalent sets

A={1,2,3} , B={3,2,1} are equal and equivalent set
A={1,2,3} , B={5,6,7} are not equal but equivalent set.

Complement of a Set-
It contains all elements of Universal set except that of a given set.

U={1,2,3,4,5,6,7,8,9}
A={2,4,6,8}
A’={1,3,5,7,9}

A’=U-A

Power of Set-

It refers to all possible sets which are subsets of a given set.
A ={1,2,3}
{} {1} {2} {3} {1,2} {1,3} {2,3} {1,2,3}
i.e 8.

Power of set is 2n Where n is number of element.

Set of Numbers-

Natural numbers N = {1, 2, 3, …}
Whole numbers W = {0, 1, 2, 3, …}
Integers Z = {…, -2, -1, 0, 1, 2, …}
Positive Integers Z+ = {1, 2, 3, 4, …}
Prime numbers P = {2, 3, 5, 7, 11, …}
Odd numbers O = {1, 3, 5, 7, …}
Real numbers R = {2, 4.3, -4, 67.3, …}
Rational Numbers ={2,¾,½, 5,..}

Function & Relation -
What is Relationship?
What is Function?
Domain & Range
Types of Function
Types of Relationship

Types of function -

One-One
Onto or Surjective
Bijection
Identity
Into
Constant
Equal
Inverse
Composite


Notes


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