3. Venn Diagram.pptx

Venn Diagram

1. Venn Diagram Discrete Mathematics

2. What is a Venn Diagram A diagram that consists of circles. The circles represent the elements of the set, and the outer parts represent elements that are not part of the set. A Venn Diagram is used to organize a list of data.

3. History of Venn Diagram Venn diagrams were introduced around 1880 by John Venn. They are used to teach elementary set theory. (*Set theory is the branch of mathematics that studies sets, which are collections of objects) It is also used to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science

4. History of Venn Diagram Venn diagrams were introduced around 1880 by John Venn. They are used to teach elementary set theory. (*Set theory is the branch of mathematics that studies sets, which are collections of objects) It is also used to illustrate simple set relationships in probability, logic, statistics, linguistics and computer science

5. Venn diagram glossary Set - A collection of things. Given the versatility of Venn diagrams, the things can really be anything. The things may be called items, objects, members or similar terms.

6. Venn diagram glossary Union - All items in the sets.

7. Example - Union If A = {2, 5, 7} and B = {1, 2, 5, 8}. Find A U B using V enn D iagram. Therefore, from the Venn diagram we get A U B = {1, 2, 5, 7, 8}

8. Example - Union From the adjoining figure find A union B. Therefore, from the Venn diagram we get A U B = {0, 1, 2, 3, 5, 8, 9 }

9. Activity - Union If A = {1, 2, 3, 6, 9, 18} and B = {1, 2, 3, 4, 5}. Find A U B using V enn D iagram. If B = {1, 2, 3, 4, 5} and A = {2, 4, 6, 8}. Find A U B using V enn D iagram. Let A = {1, 2} and B = {2, 3}. Find A U B using V enn D iagram.

10. Activity - Union Find the elements of the Sets. A= B= AUB =

11. Venn diagram glossary Intersection - The items that overlap in the sets. Sometimes called a subset.

12. Example - Intersection If A = {1, 2, 3, 4, 5} and B = {1, 3, 9, 12}. Find A ∩ B using V enn diagram. Therefore, from the V enn diagram we get A ∩ B = {1, 3}

13. Example - Intersection From the adjoining figure find A intersection B. Therefore, from the V enn diagram we get A ∩ B = {p, q, m}

14. Activity - Intersection If A = {1, 2, 3, 6, 9, 18} and B = {1, 2, 3, 4, 5}. Find A ∩ B using V enn D iagram. If P = {3, 6, 9, 12, 15, 18} and Q = {2, 4, 6, 8, 10, 12, 14}. Find P ∩ Q using V enn D iagram. Let A = {a, e, i , o, u} and B = {z, v, x, a, o}. Find A ∩ B using V enn D iagram.

15. Venn diagram glossary Symmetric difference of two sets - Everything but the intersection. Let A and B are two sets. The symmetric difference of two sets A and B is the set (A – B) ∪ (B – A) and is denoted by A △ B.

16. Example - Symmetric difference  If A = {1, 2, 3, 4, 5, 6, 7, 8} and B = {1, 3, 5, 6, 7, 8, 9}, then A – B = {2, 4}, B – A = {9} and A  △  B = {2, 4, 9}. Therefore, the shaded part of the Venn diagram represents A △ B = {2, 4, 9}.

17. Example - Symmetric difference    If A = {1, 2, 4, 7, 9} and B = {2, 3, 7, 8, 9} then A △ B = {1, 3, 4, 8} Therefore, the shaded part of the Venn diagram represents A △ B = {1, 3, 4, 8}.

18. Activity - Symmetric difference If P = {a, c, f, m, n} and Q = {b, c, m, n, j, k} . Find P △ Q using Venn Diagram. 2. Suppose there are two sets with some elements. Set A = {1, 2, 3, 4, 5} Set B = {3, 5} Find A △ B using Venn Diagram.

19. Venn diagram glossary Absolute complement - Everything not in the set.

20. Venn diagram glossary Relative complement  - In one set but not the other.

21. Venn diagram glossary Relative complement  - In one set but not the other.