GCSE · Venn diagrams & set notation

Set notationExam-style questions

The formal language of sets — the universal set ξ, n(A) for a count, union A∪B ("in either, or both"), intersection A∩B, the complement A′, and combined expressions such as A∩B′ and (A∪B)′ — read as names for regions of a Venn diagram.

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11 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
There are $30$ students in a class.

$W$ is the set of students who walk to school and $L$ is the set of students who have a school lunch.

The Venn diagram shows the numbers of students inside the circles. The number of students outside both circles has been left off.(a) Write down $n(W \cap L')$ .

(b) Find $n\big((W \cup L)'\big)$ .

(c) Explain why $n(W' \cap L')$ must give the same answer as part (b), without doing a second calculation.
Level 4 · 5 marksTry it
2
$\xi$ is the set of the $50$ members of a running club.

$A$ is the set of members who have run a marathon.

$B$ is the set of members who have run a half marathon.

$n(A) = 26$ , $n(B) = 21$ and $n(A \cap B) = 8$ .

(a) Find $n(A \cup B)$ .

(b) Find $n(A \cap B')$ .

(c) Find $n(A' \cap B')$ .
Level 4 · 5 marksTry it
3
$40$ members of a sports club were asked which of football ( $F$ ), netball ( $N$ ) and tennis ( $T$ ) they play.

The Venn diagram shows the results.(a) Write down $n(F \cap N)$ .

(b) Find $n(F \cup T)$ .

(c) Write down $n(F \cap N \cap T')$ .

(d) Find $n(N')$ .
Level 4 · 6 marksTry it