Set operations and Venn Diagrams. COPYRIGHT 2006 by LAVON B. PAGE

Transcription

1 Set operations and Venn Diagrams

2 Set operations and Venn diagrams! = { x x " and x " } This is the intersection of and. # = { x x " or x " } This is the union of and. n element of! belongs to both and, an element of # is required to belong to at least one of the sets.

3 ! = { x x " and x " }

4 # = { x x " or x " }

5 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram.

6 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. C

7 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. 1 C

8 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. 2 1 C

9 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region C

10 Sets and the Universal Set = {1,2,3,4}, = {1,3,5,7}, and C = {7,9,3}, and the universal set U = {1,2,3,4,5,6,7,8,9}. Locate all this information appropriately in a Venn diagram. With each number, place it in the appropriate region. Check out the Venn diagram and make sure you agree with where all the elements have been placed C

11 Distributive Law for Unions # (! C) = ( # )! ( # C)

12 Distributive Law for Unions # (! C) = ( # )! ( # C) C

13 Distributive Law for Unions # (! C) = ( # )! ( # C) C ( # )! ( # C)

14 Distributive Law for Unions # (! C) = ( # )! ( # C) C # (! C) C ( # )! ( # C)

15 Distributive Law for Unions # (! C) = ( # )! ( # C) C # (! C) C ( # )! ( # C)

16 DeMorgan s Law ( # ) c = c! c

17 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture

18 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture t this stage is painted green.

19 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture Now is painted red, so what s outside of and outside of hasn t been painted.

20 DeMorgan s Law ( # ) c = c! c ( # ) c is the gray region in this picture What hasn t been painted is c! c

21 DeMorgan s Other Law (! ) c = c # c

22 DeMorgan s Other Law (! ) c = c # c

23 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (a) students studying math but not business

24 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (a) students studying math but not business M! c

25 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (b) students studying both math and business

26 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (b) students studying both math and business M!

27 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (c) students studying either math or business

28 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (c) students studying either math or business M #

29 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (d) students who study neither math nor business

30 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (d) students who study neither math nor business (M # ) c or M c! c

31 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (e) students who don t study math and who don t study business

32 Grouping Students Let s denote by M and the students in a particular university that are studying mathematics and business. Write down the set that describes each of the following groups of students: (e) students who don t study math and who don t study business (M # ) c or M c! c

33 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C

34 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C

35 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C

36 Sketching regions representing sets: Sketch the region corresponding to the set ( # c )! C C