What does A ∩ B mean?

everything in both A and B. The intersection is the overlap.

A = {2, 4, 6} and B = {4, 6, 8}. What is A ∪ B?

{2, 4, 6, 8}. The union lists everything in either set, once.

Which symbol means the empty set?

∅. It is a set with nothing in it.

Of 20 people, 12 like tea, 10 like coffee and 5 like both. How many like neither?

3. 12 + 10 − 5 = 17 like at least one; 20 − 17.

Sets and Venn diagrams · Cambridge IGCSE Mathematics

In plain words

A set is just a collection of things: the even numbers, the students who play football. A Venn diagram draws sets as overlapping circles. Whatever is in both sets goes in the overlap.

Three things to know

∈ means "is a member of". n(A) is the number of things in set A. ∅ is the empty set. A′ is everything not in A.
A ∩ B (intersection) is what is in both. A ∪ B (union) is what is in A or B or both. A ⊂ B means A is inside B.
Fill in a Venn diagram from the middle outwards: the overlap first.

Worked example

In a class of 30, 18 play football, 15 play tennis and 5 play neither. How many play both?

30 − 5 = 25 students play at least one sport.
18 + 15 = 33, which counts the students who play both twice.
33 − 25 = 8 play both.

Tips and tricks

∩ looks like an "n" for "and": in both. ∪ looks like a "u" for "union": in either.
In Venn diagram questions, the number given for a set usually includes the overlap. Subtract the overlap to get "only".

5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Sets and Venn diagrams: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

What does A ∩ B mean?
- everything in A or B
- everything in both A and B (the answer)
- everything not in A
- the number of things in A
The intersection is the overlap.
A = {2, 4, 6} and B = {4, 6, 8}. What is A ∪ B?
- {4, 6}
- {2, 4, 6, 8} (the answer)
- {2, 8}
- {2, 4, 4, 6, 6, 8}
The union lists everything in either set, once.
A = {a, b, c, d}. What is n(A)?
- 1
- 3
- 4 (the answer)
- 26
There are four members.
Which symbol means the empty set?
- ∈
- ∅ (the answer)
- ∪
- ⊂
It is a set with nothing in it.
Of 20 people, 12 like tea, 10 like coffee and 5 like both. How many like neither?
- 0
- 3 (the answer)
- 5
- 8
12 + 10 − 5 = 17 like at least one; 20 − 17.

5 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

3 questions, 7 marks. Write your answers on paper, then check them.

Sets and Venn diagrams

Cambridge IGCSE Mathematics 0580 · 7 marks · papermunch.org

Name ______________________________ Date ______________

A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7}. List the members of A ∩ B and of A ∪ B.[2]
Show answerHide answer
A ∩ B = {4, 5}. A ∪ B = {1, 2, 3, 4, 5, 6, 7}.
I got this one
The universal set is the whole numbers from 1 to 10, and A is the even numbers. List A′ and state n(A).[2]
Show answerHide answer
A′ = {1, 3, 5, 7, 9}. n(A) = 5.
I got this one
Of 40 students, 25 study French, 20 study Spanish and 8 study both. How many study neither?[3]
Show answerHide answer
3. 25 + 20 − 8 = 37 study at least one; 40 − 37.
I got this one

Answers: Sets and Venn diagrams

1. A ∩ B = {4, 5}. A ∪ B = {1, 2, 3, 4, 5, 6, 7}.
2. A′ = {1, 3, 5, 7, 9}. n(A) = 5.
3. 3. 25 + 20 − 8 = 37 study at least one; 40 − 37.