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# Venn Diagrams - PowerPoint PPT Presentation

Venn Diagrams. EQ: How do I use a Venn diagram to represent different sets of numbers and to solve problems?. B. A. U. A. B. U. A. B. U. Disjoint Sets. U. A B =. Disjoint and Exhaustive. U = {x|-3<x<8, x } A and B are subsets of U, A={x|x<5} and B = {x|x 5}.

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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

U

B

U

B

U

U

AB =

U = {x|-3<x<8, x }

A and B are subsets of U, A={x|x<5} and B = {x|x 5}

U={1,2,3,4,5,6,7,8}A = 1,3,6,8 B = {2,3,4,5,8}

A

B

U

U={1,2,3,4,5,6,7,8}A = {1,3,6,7,8} B = {3,6,8}

A

B

U

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

P

(7)

(11)

(3)

(4)

U

Example 1

• Given the Venn Diagram below, how many elements are there in

• P

• P U Q

• Q’

• P, but not Q

• Q, but not P

• neither P nor Q?

X

(8)

(3)

(6)

(2)

U

YOU DO:

• Give the number of elements in:

• X’

• X Y

• X U Y

• X, but not Y

• Y, but not X

• Neither X nor Y

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

A

(a)

(c)

(b)

(d)

U

YOU DO:

• Given n(U) = 26, n(A) = 11, n(B) = 12 and n(A B) = 8, find:

• n(A U B)

• n(B, but not A)

• n(A’)

15

4

15

b = 8

a + b = 11; a = 3

b + c = 12; c = 4

a + b + c + d = 26

3 + 8 + 4 + d = 26; d = 11

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

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

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

• 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

• 4a – pg 78 #1; #4; pg 79 #7,

pg 80 #9

• 4b – pg 81, 82 #11 - 14