Unit 10 – Logic and Venn Diagrams

1. Unit 10 – Logic and Venn Diagrams

2. Unit 10 – Logic and Venn Diagrams Venn Diagram: Example

3. Using the numbers 0, 1, 2, … , 9 illustrate the sets: and Solution: Use a Venn diagram

4. Using the numbers 0, 1, 2, … , 9 illustrate the sets: and 4 A B 4 is in BOTH sides

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

6. 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

7. 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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9. Unit 10 – Logic and Venn Diagrams Venn Diagram: Key Definitions

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

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

12. Complementary: Members not in the set A A’

13. Universal Set: All members U

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

15. Number of elements in a set: Empty set:

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

18. U A B

19. U A B

20. U A B

21. U A B

22. U A B

23. U A B

24. U A B

25. U A B

26. U A B

27. U A B

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

30. What is the shaded region? U A B

31. What is the shaded region? U A B

32. What is the shaded region? U A B

33. What is the shaded region? U B A C

34. What is the shaded region? U B A C

35. What is the shaded region? U B A C

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

38. 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

39. 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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