Unit 10 – Logic and Venn Diagrams

Presentation 1 Venn Diagrams: ExamplePresentation 2 Venn Diagrams: Key DefinitionsPresentation 3 Venn Diagrams: Illustrating SetsPresentation 4 Venn Diagrams: Theoretical ExamplePresentation 5 Venn Diagram: Practical Example

Unit 10 – Logic and Venn DiagramsVenn Diagram: Example

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and

Solution: Use a Venn diagram

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and

A B

4 is in BOTH sides

4

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and

A B

7 and 9 are only in set A

47

9

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and

A B

1, 2, 3 and 5 are only in set B

47

9

1

23

5

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and

A B

0, 6 and 8 are not in A or B

47

9

1

23

5

0

6

8

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Venn Diagrams: Example

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Return to the StartPresentation 2 Venn Diagrams: Key DefinitionsPresentation 3 Venn Diagrams: Illustrating SetsPresentation 4 Venn Diagrams: Theoretical ExamplePresentation 5 Venn Diagram: Practical Example

Unit 10 – Logic and Venn Diagrams

Venn Diagram: Key Definitions

A B

Intersection: Members of both set A and set B

A B

Union: Members of set A or set B or both

Complementary: Members not in the set

A

A’

Universal Set: All members

U

A

B

Subset: All members of set A are in set B

Number of elements in a set:

Empty set:

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Venn Diagrams: Key Definitions

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Return to the StartPresentation 1 Venn Diagrams: ExamplePresentation 3 Venn Diagrams: Illustrating SetsPresentation 4 Venn Diagrams: Theoretical ExamplePresentation 5 Venn Diagram: Practical Example

Unit 10 – Logic and Venn Diagrams

Venn Diagrams: Illustrating Sets

A B

U

A B

U

A B

U

A B

U

A B

U

A B

U

A B

U

A B

U

A B

U

A B

U

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Venn Diagrams: Illustrating Sets

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Unit 10 – Logic and Venn Diagrams

Venn Diagrams: Theoretical Example

A B

U

What is the shaded region?

A B

U

What is the shaded region?

A B

U

What is the shaded region?

A BU

What is the shaded region?

C

) C A ( B

A BU

What is the shaded region?

C

)' C B A (

A BU

What is the shaded region?

C

)B' C (A

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Venn Diagrams: Theoretical Example

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Presentation 1 Venn Diagrams: ExamplePresentation 2 Venn Diagrams: Key DefinitionsPresentation 3 Venn Diagrams: Illustrating SetsPresentation 5 Venn Diagrams: Practical Example

Unit 10 – Logic and Venn Diagrams

Venn Diagram: Practical Example

U = {Natural Numbers less than 16}

Describe set A and set BA = {Even Numbers}B = {Prime Numbers}

A B

4

10

14

6

12 8

213

57

3

11

1

15

9U

U

28

20

14

1626

1218 24

30

10

25

15

21

27

13

19

11

29

17

Describe Sets U, A, B and C

U = {10,11,12,13,14,........29,30}A = {Even Numbers}B = {Multiples of 3}C = {Multiples of 5}

C

BA

22

23

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Venn Diagrams: Practical Example

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Presentation 1 Venn Diagrams: ExamplePresentation 2 Venn Diagrams: Key DefinitionsPresentation 3 Venn Diagrams: Illustrating SetsPresentation 4 Venn Diagrams: Theoretical Example