Sets & Venn diagrams

Some students were asked if they study French (F) or Spanish (S)

The Venn diagram gives information about the results. The values shown represent numbers of students.

How many of these students study only French or only Spanish?

One of these students is chosen at random.

Find the probability that this student studies both French and Spanish.

E 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 A 2, 4, 6, 8, 10, 12 B 3, 6, 9, 12 C 1, 3, 5, 7, 9, 11

List the members of the set

A B

Bʹ

E 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 A 2, 4, 6, 8, 10, 12 B 3, 6, 9, 12 C 1, 3, 5, 7, 9, 11

Write a symbol from the box on each dotted line to make each of the following a true statement.

A C _........

13_........ E

E 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 A 2, 4, 6, 8, 10, 12 B 3, 6, 9, 12 C 1, 3, 5, 7, 9, 11

List the members of the set

A B

Bʹ

E 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 A 2, 4, 6, 8, 10, 12 B 3, 6, 9, 12 C 1, 3, 5, 7, 9, 11

Write a symbol from the box on each dotted line to make each of the following a true statement.

A C _........

13_........ E

120 gardeners were asked if they grow carrots (C) or potatoes (P) or tomatoes (T)

Of these gardeners

43 grow carrots 12 grow carrots and potatoes and tomatoes 18 grow carrots and potatoes 27 grow carrots and tomatoes 32 grow potatoes and tomatoes 29 do not grow carrots or potatoes or tomatoes

The number of these gardeners who grow only potatoes is equal to the number of these gardeners who grow only tomatoes.

Complete the Venn diagram to show this information.

Find n(T C)

One of the gardeners who grows carrots is chosen at random.

Calculate the probability that this gardener also grows potatoes.

Here is a Venn diagram.

List the members of the set B

List the members of the set A B

List the members of the set A

ℰ = {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34} A = {even numbers} B = {23, 29, 31} C = {multiples of 3}

List the members of the set

B C

A′ C

Is it true that B C = ?

Tick () one of the boxes below.

Give a reason for your answer.

The set D has 4 members and is such that D (A C) =

List the members of set D

7 ℰ = {23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34} A = {even numbers} B = {23, 29, 31} C = {multiples of 3}

List the members of the set

B C

A′ C

Is it true that B C = ?

Tick () one of the boxes below.

Give a reason for your answer.

The set D has 4 members and is such that D (A C) =

List the members of set D

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {factors of 6} B = {prime numbers}

List the members of the set

A B

A

Harpreet states that A B

Harpreet is incorrect.

Explain why.

C is a set with 4 members such that

the set A C has 2 members the set B C has 2 members

Set A C and set B C have no members in common.

List the 4 members of set C

Here is a Venn diagram.

List the members of the set

A

A B

A B

ℰ = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

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

Complete the Venn diagram for this information.

Here is a Venn diagram.

Write down the numbers that are in the set

A

B C

Dominic writes down 9 C

Explain why Dominic is correct.

Here is a Venn diagram.

Write down the numbers that are in the set

A

B C

Dominic writes down 9 C

Explain why Dominic is correct.

The Venn diagram shows a universal set ℰ and sets A, B and C

The numbers and the letter x represent numbers of elements.

Given that n(A B) = 42

find the value of x

Find n(Aʹ)

Find n(Bʹ C)

30 children were asked whether they have a cat (C) or a dog (D)

Of the 30 children

5 have both a cat and a dog 13 have a dog 11 have only a cat

Complete the Venn diagram.

One of the children is picked at random.

Find the probability that this child

has a dog,

does not have a dog and does not have a cat.

ℰ = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {even numbers} A B = {12, 16, 20} (A B)ʹ = {17, 19}

Complete the Venn diagram for the sets ℰ, A and B

3 ℰ = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

A = {even numbers} A B = {12, 16, 20} (A B)ʹ = {17, 19}

Complete the Venn diagram for the sets ℰ, A and B

A, B and C are three sets.

n(A B C) = 5 n(A B C′) = 2 n(A C) = 5 n(A) = 17 n([A B C]′) = 3 n(A′ B C′) = 6 n(B C) = 7 n(C) = 14

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

E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 3} B = {odd numbers}

List the members of the set

A B

A B

Is it true that 24 A?

Tick one of the boxes below.

Give a reason for your answer.

Set C has 4 members such that C B = {10, 18}

List the members of one possible set C

E = {9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {multiples of 3} B = {odd numbers}

List the members of the set

A B

A B

Is it true that 24 A?

Tick one of the boxes below.

Give a reason for your answer.

Set C has 4 members such that C B = {10, 18}

List the members of one possible set C

50 students have lessons at a dance school. Two of the lessons are ballet lessons (B) and tap lessons (T).

Of the 50 students

31 have ballet lessons 27 have tap lessons 18 have ballet lessons and tap lessons

Complete the Venn diagram for this information.

E = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}

A B = {5, 10, 15}

B = {7, 8, 9, 11, 12, 13, 14}

A = {4, 6, 7, 8, 14}

Complete the Venn diagram for this information.

There are 32 students in a class. In one term these 32 students each took a test in Maths (M), in English (E) and in French (F).

25 students passed the test in Maths. 20 students passed the test in English. 14 students passed the test in French. 18 students passed the tests in Maths and English. 11 students passed the tests in Maths and French. 4 students failed all three tests. x students passed all three tests.

The incomplete Venn diagram gives some more information about the results of the 32 students.

Use all the given information about the results of students who passed the test in Maths to find the value of x.

Use your value of x to complete the Venn diagram to show the number of students in each subset.

A student who passed the test in Maths is chosen at random.

Find the probability that this student failed the test in French.

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

Complete the Venn diagram below for the setsE, A and B.

One of the numbers inE is to be chosen at random.

Find the probability that this number is not in set A and not in set B.

E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

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

List the members of the set

A B

A B

E = {20, 21, 22, 23, 24, 25, 26, 27, 28, 29}

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

List the members of the set

A B

A B

E = {21, 22, 23, 24, 25, 26, 27, 28, 29, 30} A = {22, 24, 26, 28, 30} B = {21, 24, 27, 30}

List the members of the set

A B

Aʹ

C = {23, 25, 29}

Using set notation, find an expression for C in terms of A and B.

complete the Venn diagram to show the number of elements in each region.

An element is chosen at random from E.

Using the Venn diagram, find the probability that this element is in

A B

A Bʹ

E = {whole numbers from 1 to 15} A = {even numbers} B = {3, 6, 9, 12, 15}

Complete the Venn diagram for the setsE, A and B.

The numbers from 1 to 14 are shown in the Venn diagram.

List the members of the set A B

List the members of the set Bʹ

A number is picked at random from the numbers in the Venn diagram.

Find the probability that this number is in set A but is not in set B.

The numbers from 1 to 14 are shown in the Venn diagram.

List the members of the set A B

List the members of the set Bʹ

A number is picked at random from the numbers in the Venn diagram.

Find the probability that this number is in set A but is not in set B.

E= {integers x such that 10 ≤ x ≤ 25} A= {x: x 18} B= {x: 13 x 22}

Write down n(A)

List the members of the set (A B)ʹ

List the members of the set Aʹ B

C A, C B and n(C) = 5

List the members of the set C

B = {b, l, u, e}

G = {g, r, e, y}

W = {w, h, i, t, e}

List all the members of the set

B G

W G′

Serena writes down the statement B G W=

Is Serena’s statement correct? You must give a reason for your answer.

B = {b, l, u, e}

G = {g, r, e, y}

W = {w, h, i, t, e}

List all the members of the set

B G

W G′

Serena writes down the statement B G W=

Is Serena’s statement correct? You must give a reason for your answer.

E = {10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

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

Complete the Venn diagram for this information.

Some students in a school were asked the following question.

“ Do you have a dog (D), a cat (C) or a rabbit (R)?”

Of these students

28 have a dog 18 have a cat 20 have a rabbit 8 have both a cat and a rabbit 9 have both a dog and a rabbit x have both a dog and a cat 6 have a dog, a cat and a rabbit 5 have not got a dog or a cat or a rabbit

Using this information, complete the Venn diagram to show the number of students in each appropriate subset. Give the numbers in terms of x where necessary.

Given that a total of 50 students answered the question,

work out the value of x.

Find n(Cʹ Dʹ)

E = {11, 12, 13, 14, 15, 16, 17, 18, 19, 20} A = {even numbers} B = {multiples of 3}

List the members of the set

A B

A B

A މ

On the Venn diagram, shade the set (A B C

Use set notation to describe the shaded region in the Venn diagram below.

E = {positive integers less than 20} A = {x: x 12} B = {x: 7 ≤ x 16}

List the members of A B

C is a set such that C A and n(C

Given that all members of C are even numbers,

list the members of one possible set C.

E = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {2, 3, 5, 7} B = {4, 6, 8, 10}

Explain why A B =

x E and x A B

Write down the two possible values of x.

Set C is such that

A B C = E A C = {2} B C

List all the members of set C.

Here is a Venn diagram.

Write down the numbers that are in the set

A

B C

Brian writes down the statement A C = Ø

Is Brian’s statement correct? You must give a reason for your answer.

One of the numbers in the Venn diagram is picked at random.

Find the probability that this number is in set C

Here is a Venn diagram.

Write down the numbers that are in the set

A

B C

Brian writes down the statement A C = Ø

Is Brian’s statement correct? You must give a reason for your answer.

One of the numbers in the Venn diagram is picked at random.

Find the probability that this number is in set C

The Venn diagram shows the numbers in the universal set, E, and two sets A and B.

List the members of the set

A

A B

A number is picked at random from the universal set.

Find the probability that this number is in set B but not in set A.

The Venn diagram shows a universal set, E, and sets A, B and C.

7, 3, 8, 1, 4 and 9 represent the numbers of elements.

Find

n(A B)

n(C)

n( )