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

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Transcription:

Set operations and Venn Diagrams

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.

! = { x x " and x " }

# = { x x " or x " }

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.

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

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

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

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 3 C

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. 2 6 8 4 1 3 9 5 7 C

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

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

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

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

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

DeMorgan s Law ( # ) c = c! c

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

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

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.

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

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

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

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

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

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

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!

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

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 #

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

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

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

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

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

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

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

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