# CPT Chapter Sets Functions and Relations

*With Anand.Duration:3hrs32min*

Set ,Function, Relationship & Venn Diagram | Duration (min:sec) |

Set | |

Overview & Index of Set | 03:47 |

What is Set | 08:34 |

How are Set Displayed | 10:28 |

Operations of Set | 11:48 |

Types of Set | 13:50 |

Compliment of Set | 04:38 |

Power of Set | 05:28 |

Union & Intersection | 04:42 |

Properties of Union & Intersection | 28:03 |

Set of Numbers | 06:01 |

Product Set | 04:11 |

Conclusion | 02:21 |

Functions & Relationship | |

Index | 02:00 |

What is relationship & Function | 10:47 |

Solving Function | 11:21 |

Domain & Range | 07:46 |

Types of Functions | 09:38 |

Solving Types of Function | 19:14 |

Types of Relationship | 12:03 |

Venn Diagram | 08:15 |

Final Quiz | 26:46 |

Conclusion | 00:56 |

Total | 03:32:37 |

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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