Venn Diagrams
Numbers in each region
Example 1

a)
b)
c)
d)
e)
f)
Given the Venn
Diagram below, how
many elements are
there in
P
PUQ
Q’
U
P, but not Q
Q, but not P
neither P nor Q?
Q
P
(7)
(3)
(11)
(4)
YOU DO:

a)
b)
c)
d)
e)
f)
Give the number
of elements in:
X’
X  Y
XUY
X, but not Y
Y, but not X
Neither X nor Y
Y
X
(8)
U
(6)
(3)
(2)
6 + c = 17 ; c = 11
Example 2:
11
8 + 6 + 11 + d = 30
25 + d = 30 ; d = 5
Given n(U) = 30, n(A) = 14,
n(B) = 17 and n(A  B) = 6 find:
a) n(A U B) 25
A
b) n(A, but not B)
5

•b=6 6
8
• a + b = 14 a + 6 = 14
• b + c = 17 a = 8
8
• a + b + c + d = 30
(a)
U
(b)
B
(c)
(d)
YOU DO:

a)
b)
c)
Given n(U) = 26, n(A) = 11, n(B) = 12
and n(A  B) = 8, find:
n(A U B) 15
B
A
n(B, but not A) 4
(a)
(c)
(b)
n(A’) 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
U
(d)
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
(a)
(b)
(c)
Brown a + b + c + d = 27
a + b = 19 a = 8
b + c = 14 c = 3
b = 11
U
(d)
d=5
YOU DO:
Pele has 14 cavies as pets. Five have long hair and 8 are
brown. Two are both brown and have long hair.
a)
Place this information on a Venn diagram
b)
Find the number of cavies that:
a) Are short haired c + d = 9
b) Have short hair and are brown c = 6
c) Have short hair and are not brown d = 3
Long
Brown
a + b + c + d = 14 d = 3
a+b=5
(a)
(b)
(c)
b+c=8
b=2
U
(d)
a=3
c=6
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
4m
1. a + b + c + d = 25
2. a + b = 18
(a)
(b)
(c)
3. b + c = 17
18 + c + 0 = 25
U
(d)
c=7
Therefore b + 7 = 17 and b = 10
Now for the real real
thing…
b)
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
c)
Newspaper A or B but not C

a)
A
a = 3; a + d = 8; a + b = 11; a + c = 13
Therefore, d = 5, b = 8, and c = 10
d
g
c
g + 3 + 5 + 10 = 36; therefore g = 36
a
f
e + 3 + 5 + 8 = 40; therefore e = 24
f + 3 + 8 + 10 = 32; f = 31 and h = 1
B
U
e
b
C
HW #4
4a – pg 78 #1; #4; pg 79 #7,
pg 80 #9
 4b – pg 81, 82 #11 - 14
