Venn diagrams and set notation

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

P = {prime numbers}

O = {odd numbers}

1. List the members of P ∩ O.
2. List the members of P ∪ O.
3. List the members of P′.

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

A = {even numbers}   B = {multiples of 5}

Kim draws a Venn diagram. She puts:

2, 4, 8 in A only   6, 10 in the intersection of A and B   5 in B only   1, 3, 9 outside both circles.

Write down two mistakes Kim has made.

A = {factors of 12}   B = {factors of 18}

1. List the members of A ∩ B.
2. Is 9 a member of A ∪ B? Give a reason for your answer.

ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

A = {multiples of 3}   B = {even numbers}

Complete the Venn diagram.

40 people were asked whether they drink coffee (C) and whether they drink tea (D).

14 drink coffee only, 6 drink both, 11 drink tea only and 9 drink neither.

One of the 40 people is chosen at random.

1. Find the probability that this person drinks both coffee and tea.
2. Find the probability that this person drinks coffee or tea or both.

ξ = {integers from 1 to 12}

A = {even numbers}

B = {factors of 12}

1. List the members of A ∩ B.
2. List the members of A ∪ B.
3. Work out n((A ∪ B)′).

30 students were asked whether they play football (F) or hockey (H). 18 play football, 12 play hockey and 5 play neither.

1. How many students play both?
2. How many play football only?
3. One student is chosen at random. Find the probability that they play hockey only.

There are 50 students in a year group.

23 study geography (G).

19 study history (H).

8 study both geography and history.

Complete the Venn diagram to show the number of students in each region.

ξ = {odd numbers between 0 and 20}

A = {multiples of 3}   B = {numbers less than 10}

Draw a Venn diagram to show the sets A and B, putting every member of ξ in the correct region.

A gym has 80 members.

47 members use the treadmill (T).

39 members use the weights (W).

21 members use both the treadmill and the weights.

1. Complete the Venn diagram to show the number of members in each region.
2. One of the 80 members is chosen at random. Work out the probability that this member uses neither the treadmill nor the weights.

60 people were asked whether they have a dog (D) or a cat (C).

32 people have a dog.

27 people have a cat.

11 people have both a dog and a cat.

1. Work out the number of people who have a dog but not a cat.
2. Work out the number of people who have neither a dog nor a cat.
3. One of the 60 people is chosen at random. Work out the probability that this person has a dog but not a cat.

The Venn diagram regions for sets A and B contain these numbers of people:

A only: 7   A ∩ B: 5   B only: 8   outside both: 10

One of the people is chosen at random.

1. Find P(A ∩ B).
2. Find P(A′).
3. Find P(A ∪ B).