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## PowerPoint Slideshow about 'Venn Diagrams' - elewa

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### Venn Diagrams

EQ: How do I use a Venn diagram to represent different sets of numbers and to solve problems?

A

B

U

Four regions on a Venn Diagram- In A, but not in B
- In B, but not in A
- In both A and B
- Neither in A nor B

B

A

6 + c = 17 ; c = 11

11

Example 2:8 + 6 + 11 + d = 30

25 + d = 30 ; d = 5

5

- Given n(U) = 30, n(A) = 14,

n(B) = 17 and n(A B) = 6 find:

- n(A U B)
- n(A, but not B)

25

8

(a)

(c)

- b = 6
- a + b = 14
- b + c = 17
- a + b + c + d = 30

6

(b)

a + 6 = 14

a = 8

8

(d)

U

Black

Brown

(a)

(c)

(b)

(d)

U

Now, the real thing…- A squash club has 27 members. 19 have black hair, 14 have brown eyes and 11 have both black hair and brown eyes.
- Place this information on a Venn Diagram
- Find the number of members with:
- Black hair or brown eyes
- Black hair, but not brown eyes

d = 5

a + b + c + d = 27

a + b = 19

b + c = 14

a = 8

c = 3

b = 11

Long

Brown

(a)

(c)

(b)

(d)

U

YOU DO:Pele has 14 cavies as pets. Five have long hair and 8 are brown. Two are both brown and have long hair.

- Place this information on a Venn diagram
- Find the number of cavies that:
- Are short haired
- Have short hair and are brown
- Have short hair and are not brown

c + d = 9

c = 6

d = 3

a + b + c + d = 14

a + b = 5

b + c = 8

b = 2

d = 3

a = 3

c = 6

10 m

4 m

(a)

(c)

(b)

(d)

U

A little bit different…- A platform diving squad of 25 has 18 members who dive from 10 m and 17 who dive from 4 m. How many dive from both platforms?

- a + b + c + d = 25
- a + b = 18
- b + c = 17
- 18 + c + 0 = 25
- c = 7
- Therefore b + 7 = 17 and b = 10

Now for the real real thing…

- A city has three newspapers A, B, and C. Of the adult population, 1% read none of these newspapers, 36% read A, 40% read B, 52% read C, 8% read A and B, 11% read B and C, 13% read A and C and 3% read all three papers. What percentage of the adult population read:
- Newspaper A only
- Newspaper B or Newspaper C
- Newspaper A or B but not C

A

B

d

d

g

g

e

a = 3; a + d = 8; a + b = 11; a + c = 13

Therefore, d = 5, b = 8, and c = 10

g + 3 + 5 + 10 = 36; therefore g = 36

e + 3 + 5 + 8 = 40; therefore e = 24

f + 3 + 8 + 10 = 32; f = 31 and h = 1

a

a

c

c

b

b

b

b

b

f

f

f

C

U

U

U

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