2. VENN DIAGRAMS By Felicia Wright

3. QUESTIONS
What is a Venn diagram?
What are the different ways of drawing a Venn diagram?
Where did the name ‘Venn Diagram’ come from?
How do we represent the following on Venn diagrams:

4. universal set
subset
complements of sets
disjoint sets

5. WHAT IS A VENN DIAGRAM?
THEY SAY A PICTURE IS WORTH A THOUSAND WORDS… A VENN DIAGRAM IS A PICTURE REPRESENTING ONE OR MORE SETS.

6. WHERE DID THE TERM ‘VENN DIAGRAM’ COME FROM?
DO YOU KNOW? THE NAME ‘VENN’ CAME FROM AN ENGLISH MAN WHO FIRST USED THESE DIAGRAMS AS A WAY OF REPRESENTING THE RELATIONSHIP AMONG SETS. FIND OUT SOME MORE ABOUT JOHN VENN BY DOING A MINI RESEARCH ON HIM!

7. HOW DO WE USE VENN DIAGRAMS?
USING VENN DIAGRAMS…
HOW DO WE USE VENN DIAGRAMS?

8. Representing Universal Sets
Do you remember what a Universal set is?
How do we use Venn Diagrams to represent Universal Sets?

9. A UNIVERSAL SET A UNIVERSAL SET IS NORMALLY REPRESENTED BY A RECTANGLE

10. THE SHADED REGION REPRESENTS THE UNIVERSAL SET
THE SHADED REGION REPRESENTS THE UNIVERSAL SET. THE SYMBOL ‘U’ IS PLACED ON THE UPPER EDGE OF THE RECTANGLE.

11. A SET WITHIN A UNIVERSAL SET

12. LET US LOOK AT AN EXAMPLE.
EACH SET IS A SUBSET OF ITS UNIVERSAL SET AND IS NORMALLY REPRESENTED BY A CIRCLE OR LOOP IN A RECTANGLE.
LET US LOOK AT AN EXAMPLE.

13. The Venn diagram below represents the set A={2,4,6,8}
The Venn diagram below represents the set A={2,4,6,8}. Which is a subset of U U . 2 4 6 8

14. COMPLEMENT OF A SET
DO YOU REMEMBER WHAT THE COMPLEMENT OF A SET IS? HOW DO YOU THINK WE WOULD REPRESENT THIS ON A VENN DIAGRAM?

15. WHAT DOES THE SHADED REGION REPRESENT?U C

16. LET US LOOK AT AN EXAMPLEC
9 5 7 1 3 5 2 4 6 8

17. WHAT ARE THE ELEMENTS IN C’

18. HOW DO WE REPRESENT SUBSETS? ANYONE WANTS TO GIVE IT A TRY?

19. U SUBSETS CONTINUE…. B A S
WHAT CAN WE SAY ABOUT THE VENN DIAGRAM ABOVE?

20. A C B WHAT CAN WE SAY ABOUT THE VENN DIAGRAM ABOVE?
LET US LOOK AT IT AGAIN?
A IS A PROPER SUBSET OF B. HOW DO WE WRITE THIS?
A C B

21. EACH ELEMENT OF SET A IS ALSO AN ELEMENT OF SET B
EACH ELEMENT OF SET A IS ALSO AN ELEMENT OF SET B. A AND B ARE BOTH PROPER SUBSETS OF U

22. WHAT ARE PROPER SUBSETS?
DO YOU REMEMBER?
WHAT ARE PROPER SUBSETS?

23. DISJOINT SETS The set of odd numbers less than 10 {1,3,5,7,9}
WHAT ARE DISJOINT SETS?
DISJOINT SETS HAVE NO COMMON ELEMENTS.
THAT IS THEY HAVE NOTHING IN COMMON.
FOR EXAMPLE:
The set of odd numbers less than 10 {1,3,5,7,9}
And the set of even numbers less than 10 {2,4,6,8,}

24. As you have noticed these two sets have nothing in common
As you have noticed these two sets have nothing in common. Can you think of any other pairs of disjoint sets. How do we represent this on a Venn diagram?

25. VENN DIAGRAM REPRESENTING DISJOINT SETSU A B

26. WE WILL NOW LOOK AT VENN DIAGRAMS SHOWING THE UNION AND INTERSECTION OF SETS.

27. UNION AND INTERSECTION OF SETS
If two sets A and B are disjoint, A intersection B is an empty set. Sets A and B have no common elements.
That is A n B ={ } or A n B = Ø.
If two sets A and B disjoint, A union B is the set of all the elements in A and in B.
That is A U B ={Elements in A and elements in B}
LET US LOOK AT AN EXAMPLE:

28. B A U VENN DIAGRAM REPRESENTING DISJOINT SETS
THE SHADED REGION ABOVE REPRESENTS A U B A B

29. U SUBSETS B A S WHAT COLOUR IS USED TO IDENTIFY THE REGION A n B?
WHAT CAN WE SAY ABOUT THE VENN DIAGRAM ABOVE?

30. SUBSETS U
S SINCE A IS A PROPER SUBSET OF B THEN A n B = A. B A

31. SUBSETS U
S SINCE A IS A PROPER SUBSET OF B THE UNION OF A AND B CONSIST OF ALL THE ELMENTS IN B .THUS A u B = B. B A

32. Intersecting Sets U
Can you identify the union and intersection of the sets above?

33. Intersecting Sets U
THE SHADED BLACK REGION ABOVE REPRESENTS A U B

34. INTERSECTING SETS
If two sets A and B intersect, the intersection of A and B is the set of elements that are common to both A and B.
If two sets A and B intersect, the union of A and B is the set of elements that are either in set A or set B, or both sets A and B.

35. Let us look at an example:
Given that M={ Natural numbers less than 12} And N={Prime numbers less than 20} Represents this on a Venn Diagram.

36. ACTIVITY
PLEASE COMPLETE EXERCISE 4M #1,3 and Activity 14 # 1 IN YOUR TEXT. YOU MAY WORK IN PAIRS!!! PLEASE REMEMBER YOUR TEST ON FRIDAY.