Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters,...
-
Upload
devin-heath -
Category
Documents
-
view
224 -
download
2
Transcript of Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters,...
![Page 1: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/1.jpg)
Set TheoryA set is a collection of objects, or
elements. Sets are represented by capital letters, and elements by lower
case (usually).
7,5,3,1A Set A contains elements 1, 3, 5, and 7.
*elements do not need to go in any particular order*there are many ways to represent certain sets
![Page 2: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/2.jpg)
A set with no elements is called an empty set (null
or void).
A A
Set A, in either case, represents the empty set.
It’s empty! Noooo!
![Page 3: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/3.jpg)
A universal set is the set of ALL elements.
everythingA
Set A represents the universal set.
I want everything!
![Page 4: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/4.jpg)
The union of sets (A U B) is the set of all elements in A or B.
5,2,1A 9,3,1B
9,5,3,2,1AUB
The union of two students’ math skills!
![Page 5: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/5.jpg)
The intersection of sets (A B) is the set of all elements in A and B.
5,2,1A 9,3,1B
1BAOur intersection will be that sandwich if you SHARE it!
![Page 6: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/6.jpg)
When working with sets, Venn Diagrams become very useful in determining the
truth of statements.
A
B CDo you swear to tell the truth, the whole truth, and
nothing but the truth?
![Page 7: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/7.jpg)
The shaded region represents all of set A.
C
A
B
![Page 8: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/8.jpg)
The shaded region represents all of set B.
C
A
B
![Page 9: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/9.jpg)
The shaded region represents all of set C.
C
A
B
![Page 10: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/10.jpg)
The shaded region represents
C
A
B
CA
![Page 11: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/11.jpg)
The shaded region represents
C
A
B
BA
![Page 12: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/12.jpg)
The shaded region represents
C
A
B
)( CBA
![Page 13: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/13.jpg)
The shaded region represents
C
A
B
)()( CABA
![Page 14: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/14.jpg)
Notice and
C
A
B
)()( CABA )( CBA are the same!
C
A
B
![Page 15: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/15.jpg)
When working with sets, Venn Diagrams become very useful in determining the truth of
statements.
The Venn Diagrams on the previous slide showed the statement
was true. )()()( CABACBA
![Page 16: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/16.jpg)
Venn Diagrams also serve as a nice way to represent data..
At a restaurant, Bella, Edward, Jacob, Alice, and Jasper were asked if they had ordered (not eaten ) any of the following: chicken marsala, lasagna, or coke.
3 people ordered chicken marsala (Edward, Alice, Jacob).2 people ordered lasagna (Bella and Jacob).3 people ordered coke (Alice, Bella, and Jasper).1 person ordered both chicken marsala and lasagna (Jacob).
![Page 17: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/17.jpg)
Jasper (coke)
chicken marsala
lasagna coke
Jasper
Alice
Edward
Bella
Jacob
Edward (chicken marsala)
Alice (chicken marsala, coke)
Bella (lasagna, coke)
Jacob (chicken marsala, lasagna)
![Page 18: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/18.jpg)
Click on the following link to view a brief video clip. Resume the
PowerPoint after.
Venn Diagram and Instruments
![Page 19: Set Theory A set is a collection of objects, or elements. Sets are represented by capital letters, and elements by lower case (usually). Set A contains.](https://reader036.fdocuments.us/reader036/viewer/2022062312/5518aa28550346a61f8b4c1c/html5/thumbnails/19.jpg)
Now go to the following website and practice working with Venn Diagrams!
Time for Fun!