Venn diagrams

Question 1

Example 1 - (1, 4, 6, 8, 10, 11, 13, 15)

A: Factors of 30
B: Factors of 16

Complete the venn diagram

Answer 1

When drawn:
AB section: 1
A section: 6, 10, 15
B section: 4, 8
Outside: 11, 13

Question 2

Example 2 -
Below is a venn diagram to show the number of pupils in a class that own certain pets
a. How many pupils own both a cat and a dog?
b. How many pupils own a cat?
c. How many pupils own a dog or a cat?
d. How many pupils don’t own a dog?

Diagram: 
Dog: 5
Cat: 8
Both: 3
Outside: 4

Answer 2

a. 3
b. 11
c. 16
d. 12

Question 3

Example 3 - 
The Venn diagram shows the number of Y10 pupils in class who either own a Nintendo switch (N) or Xbox (X)

N: 3
X: 10
Both: 4
Outside: 8

Calculate: 
P(N)
P(N n X)
P(N u X)
P(x')
P(N' n X')
P(N U X')
P(N u X')'

Answer 3

P(N)=7/25
P(N n X)=4/25
P(N u X)=17/25
P(X')=11/25
P(N' n X')=8/25
P(N u X')=15/25
P(N u X')'=10/25

Question 4

Example 4 - 
In a class some students like cheese sandwiches  (C) and ham sandwiches (H)

3 people like cheese and ham sandwiches
15 people like cheese sandwiches altogether
19 people like just ham sandwiches
There are 40 people altogether

Draw a venn diagram for the following information

Answer 4

C: 12
H: 19
Both: 3
Outside: 6

Question 5

Example 5 -

Draw a venn diagram for the following information

14 people have a dog (D)
12 people have a cat (C)
5 people have neither
There are 25 people altogether

Answer 5

D: 8
C: 6
Both: 6
Outside: 5

Note: 14 people have a dog, 12 people have a cat, and 5 people have neither. This adds up to 31, when there should only be 25 people altogether. 31-25=6. 6 people must have both a cat and a dog, so I put 6 in the middle section and minus 6 off of 12 and 14