Logic and Venn Diagrams Presentation 1 Venn Diagrams

Logic and Venn Diagrams Presentation 1 Venn Diagrams: Example Presentation 2 Venn Diagrams: Key Definitions Presentation 3 Venn Diagrams: Illustrating Sets Presentation 4 Venn Diagrams: Theoretical Example Presentation 5 Venn Diagram: Practical Example

Logic and Venn Diagrams Venn 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 4 A B 4 is in BOTH sides

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and 7 9 4 A B 7 and 9 are only in set A

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and 1 7 9 A 4 2 3 5 B 1, 2, 3 and 5 are only in set B

Using the numbers 0, 1, 2, … , 9 illustrate the sets: and 0 1 7 9 8 A 4 2 3 5 0, 6 and 8 are not in A or B 6 B

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Logic and Venn Diagrams Venn Diagram: Key Definitions

Intersection: Members of both set A and set B A B

Union: Members of set A or set B or both A B

Complementary: Members not in the set A A’

Universal Set: All members U

Subset: All members of set A are in set B A B

Number of elements in a set: Empty set:

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Logic and Venn Diagrams: Illustrating Sets

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 A B

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Logic and Venn Diagrams: Theoretical Example

What is the shaded region? U A B

What is the shaded region? U A B

What is the shaded region? U A B

What is the shaded region? B A C U

What is the shaded region? B A C U

What is the shaded region? B A C U

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Logic and Venn Diagrams Venn Diagram: Practical Example

1 10 A 9 14 4 12 6 U 3 13 2 8 15 5 7 11 B U = {Natural Numbers less than 16} Describe set A and set B A = {Even Numbers} B = {Prime Numbers}

A U B 14 28 26 12 18 24 16 22 13 21 27 20 19 30 15 10 23 11 29 25 C 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}

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