Unit 10 – Logic and Venn Diagrams

Unit 10 – Logic and Venn Diagrams

Unit 10 – 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 4 9 A B 7 and 9 are only in set A

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

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Unit 10 – 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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Unit 10 – Logic and Venn Diagrams Venn Diagrams: Illustrating Sets

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Unit 10 – Logic and Venn Diagrams Venn Diagrams: Theoretical Example

What is the shaded region? U A B

What is the shaded region? U B A C

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Unit 10 – Logic and Venn Diagrams Venn Diagram: Practical Example

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

U A B 14 12 13 21 28 18 26 24 16 27 19 30 22 20 15 23 10 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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Unit 10 – Logic and Venn Diagrams