SET Theory & Operations An Interactive Powerpoint Presented BY Abhishek Chakraborty

PowerPoint Presentation:

Set – A collection of objects example : a set of tires Element – An object contained within a set example : M y car’s left front tire

PowerPoint Presentation:

Finite set – Contains a countable number of objects Example : The car has 4 tires Infinite set - Contains an unlimited number of objects Example: The counting numbers {1, 2, 3, …}

PowerPoint Presentation:

Cardinal Number : Used to count the objects in a set Example: There are 26 letters in the alphabet Ordinal Number : Used to describe the position of an element in a set Example: The letter D is the 4 th letter of the alphabet

PowerPoint Presentation:

Equal sets – Sets that contain exactly the same elements (in any order) {A, R, T, S} = {S, T, A, R} Notation: A = B means set A equals set B

PowerPoint Presentation:

Equivalent sets – Sets that contain the same number of elements (elements do not have to be the same) {C, A, T} ~ {d, o, g} Notation: A ~ B means set A is equivalent to set B

PowerPoint Presentation:

Empty Set – A set that contains no elements Notation: { } or Universal Set – A set that contains all of the elements being considered Notation: U

PowerPoint Presentation:

Complement of a set – A set that contains all of the elements of the universal set that are not in a given set Notation: means the complement of B

PowerPoint Presentation:

A = {2, 4, 6, 8} B = {1, 2, 3, 4, …} C = {1, 2, 3, 4, 5} D = { } E = {Al, Ben, Carl, Doug} F = { 5, 4, 3, 2, 1} G = {x | x < 6 and x is a counting number} Set Builder Notation Which sets are finite? Which sets are equal to set C? Which sets are equivalent to set A? {1, 2, 3, 4, 5} n(E) = n(G) = 4 5 F, G E A, C, D, E, F, G

PowerPoint Presentation:

Is { } the same as ? Yes Is { } the same as ? No

PowerPoint Presentation:

Set B is a subset of set A if every element of set B is also an element of set A. Notation: B A W = {1, 2, 3, 4, 5} X = {1, 3, 5} Y = {2, 4, 6} Z = {4, 2, 1, 5, 3} True or False: X W Y W Z W W True False True True * The empty set is a subset of every set

PowerPoint Presentation:

Set B is a proper subset of set A if every element of set B is also an element of set A AND B is not equal to A. Notation: B A W = {1, 2, 3, 4, 5} X = {1, 3, 5} Y = {2, 4, 6} Z = {4, 2, 1, 5, 3} True or False: X W Y W Z W True False False

PowerPoint Presentation:

How many subsets can a set have? Set {a} {a, b} {a, b, c} Number of Elements 1 2 3 n Subsets Number of Subsets 2 4 8 2 n {a} ,{ } {a} ,{b} ,{ a,b } ,{ } {a} ,{b} ,{c} ,{ a,b }, { a,c } ,{ b,c } ,{ a,b,c }, { } If a set has n elements, it has 2 n subsets

PowerPoint Presentation:

How many proper subsets can a set have? Set {a} {a, b} {a, b, c} {a, b, c, d} Number of Elements 1 2 3 4 n Proper Subsets Number of Proper Subsets 1 3 7 15 2 n – 1 {a} ,{ } {a} ,{b} ,{ a,b } ,{ } {a} ,{b} ,{c} ,{ a,b }, { a,c } ,{ b,c } ,{ a,b,c }, { } If a set has n elements, it has 2 n – 1 proper subsets X X X

PowerPoint Presentation:

A Venn Diagram allows us to organize the elements of a set according to their attributes. Wings Horn HORSE – bred for magical Process PEGASYS UNICORN

PowerPoint Presentation:

U = {1, 2, 3, 4, 5, 6.5} even odd prime 1 2 3 4 5 6.5 Venn Diagram

PowerPoint Presentation:

National Library of Virtual Manipulatives Attribute Blocks small blue triangle

PowerPoint Presentation:

Set Operations The intersection of sets A and B is the set of all elements in both sets A and B notation: A B

PowerPoint Presentation:

The union of sets A and B is the set of all elements in either one or both of sets A and B notation: A B

PowerPoint Presentation:

The union of sets A and B is the set of all elements in either one or both of sets A and B notation: A B

PowerPoint Presentation:

A = {1, 2, 3, 4, 5} B = {2, 4, 6} C = {3, 5, 7} A B = A B = C B = C B = {2, 4} {1, 2, 3, 4, 5, 6} {2, 3, 4, 5, 6, 7) { } The set complement X – Y is the set of all elements of X that are not in Y A – B = C – A = {1, 3, 5} {7}

PowerPoint Presentation:

Representing sets with Venn diagrams A B A B C Three attributes 2 3 or 8 regions 1 2 3 4 1 2 3 4 5 6 7 8 Two attributes 2 2 or 4 regions

PowerPoint Presentation:

A B A A B A

PowerPoint Presentation:

A B A U B A B A B A B A B

PowerPoint Presentation:

A B A U B A B A B A B C (A U B) C A B C (A U B) C

PowerPoint Presentation:

(A U B) C A B C 1 2 3 4 5 6 7 8 A = B = C = C = A U B = (A U B) C = {1, 2, 4, 5} {2, 3, 5, 6} {4, 5, 6, 7} {1, 2, 3, 8} {1, 2, 3, 4, 5, 6} {1, 2, 3}

PowerPoint Presentation:

A U (B C) A B C A = B = C = B C = A U (B C) = {3, 6, 7, 8} {2, 3, 5, 6} {4, 5, 6, 7} {5, 6} {3, 5, 6, 7, 8} 3 7 8 6 5 4 1 2

PowerPoint Presentation:

A B 1 2 3 4 How many stars are in: Circle A Circle B Only Circle A Both A and B Either A or B Exactly one circle Neither circle Total stars = 3 5 2 1 7 6 2 9

PowerPoint Presentation:

B F Out of 20 students: 8 play baseball 7 play football 3 play both sports How many play neither sport? How many play only baseball? How many play exactly one sport? 20 3 5 4 8 8 5 5 + 4 = 9

PowerPoint Presentation:

B P G Out of 30 people surveyed: 20 like Blue 20 like Pink 15 like Green 14 like Blue and Pink 11 like Pink and Green 12 like Blue and Green 10 like all 3 colors How many people like only Pink? How many like Blue and Green but not Pink? How many like none of the 3 colors? How many like exactly two of the colors? 10 2 1 4 2 5 4 2 30 5 2 2 4 + 2 + 1 =7

You do not have the permission to view this presentation. In order to view it, please
contact the author of the presentation.

Send to Blogs and Networks

Processing ....

Premium member

Use HTTPs

HTTPS (Hypertext Transfer Protocol Secure) is a protocol used by Web servers to transfer and display Web content securely. Most web browsers block content or generate a “mixed content” warning when users access web pages via HTTPS that contain embedded content loaded via HTTP. To prevent users from facing this, Use HTTPS option.

By: dvl7 (63 month(s) ago)

heyyy....nice work..!! :)