1. Venn Diagrams
Numbers in each region

2. Example 1 Given the Venn Diagram below, how many elements are there in
P U Q Q’
P, but not Q
Q, but not P
neither P nor Q? P
(3)
(11)
(4)
(7) Q U

3. 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 X
(6)
(3)
(2)
(8) Y U

4. Example 2: Given n(U) = 30, n(A) = 14, n(B) = 17 and n(A B) = 6 find:
6 + c = 17 ; c = 11 11
Example 2:
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 A B 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

5. 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’) A
(b)
(c)
(d)
(a) B U 15 4 15
b = 8
a + b = 11; a = 3
b + c = 12; c = 4
a + b + c + d = 26
d = 26; d = 11

6. 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
Black
(b)
(c)
(d)
(a)
Brown U
d = 5
a + b + c + d = 27
a + b = 19
b + c = 14
a = 8
c = 3
b = 11

7. 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
Long
(b)
(c)
(d)
(a)
Brown U
a + b + c + d = 14
a + b = 5
b + c = 8
b = 2
d = 3
a = 3
c = 6

8. 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?
10 m
(b)
(c)
(d)
(a)
4 m U
a + b + c + d = 25
a + b = 18
b + c = 17
18 + c + 0 = 25
c = 7
Therefore b + 7 = 17 and b = 10

9. 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 = 36; therefore g = 36
e = 40; therefore e = 24
f = 32; f = 31 and h = 1 a a c c b b b b b f f f C U U U

10. HW #4
4a – pg 78 #1; #4; pg 79 #7,
pg 80 #9
4b – pg 81, 82 #